How to write answers EXAMPLE question1. A question2. D

Display the set of data in a cumulative frequency histogram.

Students’ Pets
Number of Pets	Tally	Frequency
0-1	| |	2
2-3	|	1
4-5	|	1
6-7	| |	2
8-9	| | |	3

Question 1 options:

Question 2 (5 points)

The tables show the number of points scored by two basketball teams this season.

Red Hawks Points Scored
42	59	50	37	36	43	44	38
40	56	49	52	46	47	55	31

Hurricanes Points Scored
45	40	49	42	50	46	45	37
40	42	51	48	45	43	46	47

Use a graphing calculator to construct a box-and-whisker plot for the Red Hawks’ number of points scored. Describe the shape of the distribution.

Question 2 options:

	The distribution is symmetric.
	The distribution is negatively skewed.
	The distribution is positively skewed.
	The distribution is linear.

Question 3 (5 points)

Find the mean. Round to the nearest tenth if necessary.

29, 22, 16, 10, 21, 23, 22, 29

Question 3 options:

	21.5
	20.4
	22.3
	22

Question 4 (5 points)

The table shows the grade that 4 students received on a math test. Find the bar graph that represents the grades.

Student	Marks
John	71
Tyler	60
Jack	77
Levi	60

Question 4 options:

Question 5 (5 points)

Display the set of data in a histogram.

Weekly TV Viewing
Time (hrs)	Tally	Frequency
0 – 4		3
5 – 9		14
10 – 14		7
15 – 19		12

Question 5 options:

Question 6 (5 points)

Use a graphing calculator to construct a histogram for the data, and use it to describe the shape of the distribution.

9, 12, 12, 6, 22, 32, 35, 37, 8, 4, 40, 6, 4, 10, 22, 34, 35, 29

16, 15, 13, 17, 18, 20, 13, 13, 18, 24, 23, 10, 16, 22, 10, 13, 26, 20

Question 6 options:

	negatively skewed distribution
	positively skewed distribution
	symmetric distribution
	linear skewed distribution

Question 7 (5 points)

Find the median. Round to the nearest tenth if necessary.

49, 13.9, 5.9, 16.6, 43.1, 11.2, 36.8, 43.7, 22.9, 45.1, 44.2

Question 7 options:

	36.8
	16.6
	22.9
	37.8

Question 8 (5 points)

Describe the center and spread of the data using either the mean and standard deviation or the five-number summary. Justify your choice by constructing a histogram for the data.

9, 1, 29, 10, 5, 39, 29, 4, 24, 8, 3, 33, 13, 32, 23, 32, 39, 10

18, 26, 26, 10, 9, 18, 15, 17, 12, 18, 9, 15, 9, 24, 12, 22, 20, 15

Question 8 options:

	The distribution is skewed, so use the five-number summary. range: 38, median: 16, half of the data are between 9.5 and 25
	The distribution is symmetric, so use the mean and standard deviation. mean: 17.7, standard deviation: 100

Question 9 (5 points)

Find the median. Round to the nearest tenth if necessary.

35, 24, 32, 24, 17, 33, 39, 23

Question 9 options:

	32
	24
	28
	28.5

Question 10 (5 points)

Find the mode of each set of data.

23, 30, 36, 29, 19, 33, 15, 36

Question 10 options:

	29.5
	27.6
	30.5
	36

Question 11 (5 points)

The tables show the number of points scored by two basketball teams this season.

Red Hawks Points Scored
42	59	50	37	36	43	44	38
40	56	49	52	46	47	55	31

Hurricanes Points Scored
45	40	49	42	50	46	45	37
40	42	51	48	45	43	46	47

What conclusion can you draw about the number of points scored by the Red Hawks and the Hurricanes?

Question 11 options:

	The means differ by only about 0.5, but the standard deviations show that the Hurricanes’ number of points is generally closer to the mean.
	The means differ by only about 0.5, but the standard deviations show that the Red Hawks’ number of points is generally closer to the mean.
	The means and standard deviations are very close for the Red Hawks and the Hurricanes.
	No conclusion can be made.

Question 12 (5 points)

Draw a dot plot for the set of data.

0, 3, 1, 3, 1, 2, 1, 5, 2, 0, 1, 2

Question 12 options:

Question 13 (5 points)

Display the set of data in a cumulative frequency histogram.

Students’ Pets
Number of Pets	Tally	Frequency
0-1	| | |	3
2-3	| |	2
4-5	| |	2
6-7	|	1
8-9	|	1

Question 13 options:

Question 14 (5 points)

The table shows the prices of electronics at a store. Find the dot plot with a scaled number line that represents the prices in the table.

Sale Prices ($)
$10.43	$36.05	$22.11	$48.92
$43.28	$40.66	$56.39	$27.00
$22.16	$19.45	$69.98	$34.82

Question 14 options:

Question 15 (5 points)

Find the variance. Round to the nearest tenth.

{6, 6, 7, 17, 20, 20}

Question 15 options:

	6.4
	41.2
	12.7
	1.6

Question 16 (5 points)

Find the mean. Round to the nearest tenth if necessary.

37.4, 11.7, 35.4, 18.6, 5.7, 48.8, 18.9, 30, 15.1, 26.6, 35.7, 40.2

Question 16 options:

	28
	26.6
	27
	25.8

Question 17 (5 points)

Find the range for each set of data.

71, 53, 102, 69, 100, 68, 104, 92, 90, 120, 64, 120, 71, 89, 105, 110

Question 17 options:

	66
	67
	91
	89

Question 18 (5 points)

Find the interquartile range.
6, 8, 9, 30, 30, 36, 38, 54, 64, 70, 75, 81, 93

Question 18 options:

	87
	34.5
	18.5
	53

Question 19 (5 points)

Find the mode of each set of data.

59, 48, 88, 24, 31, 76, 68, 88, 77, 18, 88

Question 19 options:

	88
	59
	60.5
	68

Question 20 (5 points)

Jason’s and Colleen’s quiz scores for the first quarter are shown in the tables below.

Jason’s Quiz Scores
13	19	18	19	17	16	18	17
14	16	11	15	19	20	18	20

Colleen’s Quiz Scores
14	11	13	14	15	12	10	11
16	12	15	12	13	13	13	14

Use a graphing calculator to construct a histogram for Jason’s quiz scores. Describe the shape of the distribution.

Question 20 options:

	The distribution is positively skewed.
	The distribution is negatively skewed.
	The distribution is symmetric.
	The distribution is linear.

University of Maryland University College Math 107 – College Algebra Quiz 5 Free Response, Multiple Choice, and Yes/No Problems, 6 Points Each. You may write answers after problems (you may use Microsoft Equation). If you prefer handwriting, prepare you answer sheet, scan it, and prepare a file in PDF format. Write an exact answers, using fractions or radicals as needed. Simplify answers if possible. 1. Given that f(x) = 55x + 22 and g(x) = x3, find (f ◦ g)(− 3). 2. Find (f ◦ g)(x) and (g ◦ f)(x) for f ( x) = 5 x − 4, g ( x) = x+4 . 5 3. Find ( f g )( x) and ( g f )( x) and the domain of each. f ( x) = 2 x + 1, g ( x) = x . 4. Choose the graph that shows a graph of a one-to-one function and its inverse (shown red and dashed). A C B D 5. Determine whether the function f ( x) = x + 2 is one-to-one. Yes 6. Find the inverse of the function f ( x) = − No 3 . x +1 2 In problems 7-8, solve radical equations. 7. x + 1 + 1 = x 8. 6x + 7 = x + 2 x 1 9. Choose the correct graph for the function y =   . 2 A B C D 10. Choose the correct graph for the function f ( x) = −0.35e− x + 3 . A B 11. Find the domain of the function H ( x) = log 7 x9 . A. All positive real numbers. B. All nonzero real numbers. C. All real numbers except 7. D. All real numbers. 12. Find the logarithm. log 5 54 C D 3 13. Find the logarithm. log10−8 14. Choose the correct graph for the function y = log8 x A B C D 15. Choose the correct graph. f ( x) = 3x is in the solid red line. f −1 ( x) = log 3 x is the dashed blue line. A B 16. For the function f ( x) = log3 ( x + 1) find: (a) The domain in interval notation (b) The vertical asymptote C D

I’m working on a algebra question and need a sample draft to help me learn.

 

solve the equation analytically

1. log(3x − 1) = log(4 − x)

I’m working on a algebra practice test / quiz and need support to help me learn.

 

3 – Suppose receiving stations A, B, and C are located on a coordinate plane at the points (1, 4), (-3, -1), and (5, 2). Let the distances from the earthquake epicenter to these stations be 2 units, 5 units, and 4 units, respectively. Where on the coordinate plane is the epicenter located?

6- Find the function g(x)=ax+b whose graph can be obtained by translating the graph of f(x)=3−x down 2 units and to the right 3 units.

8- An artist has sold a painting for $410,000. He needs some of the money in 6 months and the rest in 1 year. He can get a Treasury bond for 6 months at 2.65% and one for a year at 2.91%. His broker tells him the two investments will earn a total of $8671. How much should be invested at each rate to obtain that amount of interest? First indicate the amount to be invested at 2.65%, then indicate the amount to be invested at 2.91%. (Round your answers to the nearest whole number and do not use commas or dollar symbols in your answer.)

11- A PTA group sold homemade donuts to raise money for new computers. The donuts were sold for $7.00 per box and $0.50 for a single donut. If the PTA group raised $600 and sold 78 boxes, how many single donuts did they sell?

13- The area of a single room apartment is advertised as 171 square feet. You call the facility and are told that the length of the room is 10 feet longer than its width. Which of the following is one of the two dimensions of the room?

14- Find two numbers whose sum is 7500 and whose product is the maximum value. (Round your answer to the nearest whole number.)

20- A standard piece of notebook paper measuring 8.5 inches by 11 inches is to be made into a box with an open top by cutting equal-size squares from each corner and folding up the sides. Let x{“version”:”1.1″,”math”:”x”} represent the length of a side of each such square (in inches). Find the maximum volume of the box in cubic inches. (Round your answer to four significant digits.)

22 – The millage rate is the amount of property tax per $1000 of the taxable value of a home. For a particular county, the millage rate is 29 mil. A city within the county also imposes a flat fee of $101 per home. Which of the following models the taxable value of a home (in $1000) based on x dollars of property tax paid on the home?

28- The traditional IRA (individual retirement account) is a common tax-deferred saving plan in the United States. Eared income deposited into an IRA is not taxed in the current year, and no taxes are incurred on the interest paid in subsequent years. However, when you withdraw the money from the account after age 59.5, you pay taxes on the entire amount you withdraw.

Suppose you deposited $5000 of earned income into an IRA, you can earn an annual interest rate of 4%, and you are in a 25% tax bracket. Also, suppose that you deposit the $5000 at age 25 and withdraw it at age 60, and that interest is compounded continuously. Suppose that instead of depositing the money into an IRA, you pay taxes on the money and the annual interest. How much money will you have at age 60?

10/4/21, 1:16 PM Quiz: Section 5.2 Section 5.2 Started: Sep 30 at 2:12am Quiz Instructions Question 1 5 pts Consider the following intermediate tableau (not the Initial Simplex tableau): ⎡ P x1 x2 s1 s2 s3 RH S ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ 0 1 0 1 0 0 4 0 0 2 0 1 0 12 0 0 2 −3 0 1 6 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 1 0 −5 3 0 0 12 ⎣ ⎦ a) Determine the pivot column and the pivot element, and perform all the row operations for the entire pivot column to obtain the next new tableau. Once you have the new tableau, look at the numbers you have in the objective row and enter each one as requested in each box below. Note: Where applicable, fractions must be entered as 2/5, -1/3, and so on. Under column x1 in the objective row, you have: Under column x2 in the objective row, you have: Under column s1 in the objective row, you have: Under column s2 Under column s3 Under column RH S in the objective row, you have: in the objective row, you have: in the objective row, you have: https://unlv.instructure.com/courses/102986/quizzes/367220/take 1/9 10/4/21, 1:16 PM Quiz: Section 5.2 b) Given the new tableau that you obtained above, three interpretations are possible. In the box below, type or copy and paste whichever answer shown in boldface letters below that you think is the correct choice. 1. Enter solved if you think you have obtained the final tableau. 2. Enter ready for another set of pivot operations if you think more pivot operations are possible. 3. Enter no solution if you think the tableau has no solution. Question 2 5 pts Consider the following tableau: ⎡ P x1 x2 s1 s2 RH S ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ 0 8 8 1 0 160 0 4 12 0 1 180 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎣ 1 −5 −10 0 0 0 ⎦ a) Determine the pivot column and the pivot element, and perform all the row operations for the entire pivot column to obtain the next new tableau. Once you have the new tableau, look at the numbers you have in the objective row and enter each one as requested in each box below. Note: Where applicable, fractions must be entered as 2/5, -1/3, and so on. Under column x1 in the objective row, you have: Under column x2 in the objective row, you have: Under column s1 in the objective row, you have: https://unlv.instructure.com/courses/102986/quizzes/367220/take 2/9 10/4/21, 1:16 PM Quiz: Section 5.2 Under column s2 in the objective row, you have: Under column RH S in the objective row, you have: b) Given the new tableau that you obtained above, three interpretations are possible. In the box below, type or copy and paste whichever answer shown in boldface letters below that you think is the correct choice. 1. Enter solved if you think you have obtained the final tableau. 2. Enter ready for another set of pivot operations if you think more pivot operations are possible. 3. Enter no solution if you think the tableau has no solution. Question 3 5 pts Consider the following intermediate tableau (not the Initial Simplex tableau): ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ P x1 x2 0 0 1 0 1 0 1 0 0 s1 1 2 s2 − RH S ⎤ 1 3 2 2 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 1 1 5 2 2 2 2 −1 7 ⎦ a) Determine the pivot column and the pivot element, and perform all the row operations for the entire pivot column to obtain the next new tableau. Once you have the new tableau, look at the numbers you have in the objective row and enter each one as requested in each box below. Note: Where applicable, fractions must be entered as 2/5, -1/3, and so on. Under column x1 in the objective row, you have: https://unlv.instructure.com/courses/102986/quizzes/367220/take 3/9 10/4/21, 1:16 PM Quiz: Section 5.2 Under column x2 in the objective row, you have: Under column s1 in the objective row, you have: Under column s2 Under column RH S in the objective row, you have: in the objective row, you have: b) Given the new tableau that you obtained above, three interpretations are possible. In the box below, type or copy and paste whichever answer shown in boldface letters below that you think is the correct choice. 1. Enter solved if you think you have obtained the final tableau. 2. Enter ready for another set of pivot operations if you think more pivot operations are possible. 3. Enter no solution if you think the tableau has no solution. Question 4 5 pts Consider the following tableau: ⎡ P x1 x2 s1 s2 RH S ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ 0 1 0 1 0 7 0 1 −1 0 1 8 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎣ 1 −5 −4 0 0 0 ⎦ a) Determine the pivot column and the pivot element, and perform all the row operations for the entire pivot column to obtain the next new tableau. Once you have https://unlv.instructure.com/courses/102986/quizzes/367220/take 4/9 10/4/21, 1:16 PM Quiz: Section 5.2 the new tableau, look at the numbers you have in the objective row and enter each one as requested in each box below. Note: Where applicable, fractions must be entered as 2/5, -1/3, and so on. Under column x1 in the objective row, you have: Under column x2 in the objective row, you have: Under column s1 in the objective row, you have: Under column s2 Under column RH S in the objective row, you have: in the objective row, you have: b) Given the new tableau that you obtained above, three interpretations are possible. In the box below, type or copy and paste whichever answer shown in boldface letters below that you think is the correct choice. 1. Enter solved if you think you have obtained the final tableau. 2. Enter ready for another set of pivot operations if you think more pivot operations are possible. 3. Enter no solution if you think the tableau has no solution. Question 5 8 pts Use the simplex method to solve the following maximum problem: Maximize: P = 7x 1 + 5x 2 Subject to the constraints: https://unlv.instructure.com/courses/102986/quizzes/367220/take 5/9 10/4/21, 1:16 PM Quiz: Section 5.2 ⎧ 2x 1 + x 2 ≤ 100 ⎪ ⎪ 4x 1 + 3x 2 ≤ 240 ⎨ x1 ≥ 0 ⎪ ⎩ ⎪ x2 ≥ 0 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. x1 = x2 = P = Question 6 8 pts Use the simplex method to solve the following maximum problem: Maximize: P = 7x 1 + 12x 2 Subject to the constraints: ⎧ 2x 1 + 3x 2 ≤ 6 ⎪ ⎪ 3x 1 + 7x 2 ≤ 12 ⎨ x1 ≥ 0 ⎪ ⎩ ⎪ x2 ≥ 0 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. x1 = x2 = P = https://unlv.instructure.com/courses/102986/quizzes/367220/take 6/9 10/4/21, 1:16 PM Quiz: Section 5.2 Question 7 8 pts Use the simplex method to solve the following maximum problem: Maximize: P = 3x 1 + 2x 2 Subject to the constraints: ⎧ 2x 1 + x 2 ≤ 6 ⎪ ⎪ x 1 + 2x 2 ≤ 6 ⎨ x1 ≥ 0 ⎪ ⎩ ⎪ x2 ≥ 0 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. x1 = x2 = P = Question 8 8 pts Use the simplex method to solve the following maximum problem: Maximize: P = 6x 1 + 3x 2 + 2x 3 Subject to the constraints: https://unlv.instructure.com/courses/102986/quizzes/367220/take 7/9 10/4/21, 1:16 PM Quiz: Section 5.2 2x 1 + 2x 2 + 3x 3 ≤ 30 ⎧ ⎪ ⎪ ⎪ ⎪ 2x + 2x + x ≤ 12 ⎪ 1 2 3 ⎨x ≥ 0 1 ⎪ ⎪ ⎪ x2 ≥ 0 ⎪ ⎩ ⎪ x3 ≥ 0 and using your final tableau answer the questions below by entering the correct answer in each blank box. x1 = x2 = x3 = P = Question 9 8 pts Use the simplex method to solve the following maximum problem: Maximize: P = 2x 1 + 3x 2 Subject to the constraints: ⎧ x1 ⎪ ⎪ x1 ⎨ x1 ⎪ ⎩ ⎪ x2 + 2x 2 ≤ 30 + x 2 ≤ 20 ≥ 0 ≥ 0 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. x1 = x2 = https://unlv.instructure.com/courses/102986/quizzes/367220/take 8/9 10/4/21, 1:16 PM Quiz: Section 5.2 P = Quiz saved at 1:16pm https://unlv.instructure.com/courses/102986/quizzes/367220/take Submit Quiz 9/9 10/4/21, 1:17 PM Quiz: Section 5.3 Section 5.3 Started: Sep 30 at 2:14am Quiz Instructions Question 1 5 pts Consider the following minimum problem: Minimize: C = 6x 1 + 3x 2 Subject to the constraints: ⎧ 4x 1 + x 2 ≥ 4 ⎪ ⎪ x2 ≥ 2 ⎨ x1 ≥ 0 ⎪ ⎩ ⎪ x2 ≥ 0 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). P = [ Select ] y1 [ Select ] y1 ≤ [ Select ] y1 ≥ 0 y1 ; + + [ Select ] y2 [ Select ] [ Select ] y2 ≤ 3 y2 ≥ 0 Question 2 5 pts Consider the following minimum problem: Minimize: C = x 1 + 6x 2 https://unlv.instructure.com/courses/102986/quizzes/367207/take 1/9 10/4/21, 1:17 PM Quiz: Section 5.3 Subject to the constraints: ⎧ 2x 1 + 3x 2 ≥ 15 ⎪ ⎪ −x 1 + 2x 2 ≥ 3 ⎨ x1 ≥ 0 ⎪ ⎩ ⎪ x2 ≥ 0 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). P = [ Select ] y1 [ Select ] [ Select ] y1 ≥ 0 ; + [ Select ] y1 + [ Select ] y1 + [ Select ] y2 y2 ≤ 1 y2 ≤ 6 y2 ≥ 0 Question 3 5 pts Consider the following minimum problem: Minimize: C = 2x 1 + x 2 Subject to the constraints: ⎧ 5x 1 + x 2 ≥ 9 ⎪ ⎪ 2x 1 + 2x 2 ≥ 10 ⎨ x1 ≥ 0 ⎪ ⎩ ⎪ x2 ≥ 0 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). P = [ Select ] [ Select ] y1 y1 https://unlv.instructure.com/courses/102986/quizzes/367207/take + + [ Select ] [ Select ] y2 y2 ≤ 2 2/9 10/4/21, 1:17 PM Quiz: Section 5.3 [ Select ] y1 ≥ 0 y1 ; + [ Select ] y2 ≤ 1 y2 ≥ 0 Question 4 5 pts Consider the following minimum problem: Minimize: C = 14x 1 + 20x 2 Subject to the constraints: ⎧ x 1 + 2x 2 ≥ 4 ⎪ ⎪ 7x 1 + 6x 2 ≥ 20 ⎨ x1 ≥ 0 ⎪ ⎩ ⎪ x2 ≥ 0 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). P = [ Select ] [ Select ] [ Select ] y1 ≥ 0 ; y1 + [ Select ] y1 + [ Select ] y1 + [ Select ] y2 y2 ≤ 14 y2 ≤ 20 y2 ≥ 0 Question 5 8 pts Use the simplex method and the Duality Principle to solve the following minimum problem: https://unlv.instructure.com/courses/102986/quizzes/367207/take 3/9 10/4/21, 1:17 PM Quiz: Section 5.3 Minimize: C = 14x 1 + 20x 2 + 24x 3 Subject to the constraints: ⎧ x 1 + x 2 + 2x 3 ≥ 7 ⎪ ⎪ ⎪ ⎪ x + 2x + x ≥ 4 ⎪ 1 2 3 ⎨x ≥ 0 1 ⎪ ⎪ ⎪ x2 ≥ 0 ⎪ ⎩ ⎪ x3 ≥ 0 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. x1 = x2 = x3 = C = Question 6 8 pts Use the simplex method and the Duality Principle to solve the following minimum problem: Minimize: C = 9x 1 + 4x 2 + 10x 3 Subject to the constraints: 2x 1 + x 2 + 3x 3 ≥ 6 ⎧ ⎪ ⎪ ⎪ ⎪ 6x + x + x ≥ 9 ⎪ 1 2 3 ⎨ x1 ≥ 0 ⎪ ⎪ ⎪ x2 ≥ 0 ⎪ ⎩ ⎪ x3 ≥ 0 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. https://unlv.instructure.com/courses/102986/quizzes/367207/take 4/9 10/4/21, 1:17 PM Quiz: Section 5.3 x1 = x2 = x3 = C = Question 7 8 pts Use the simplex method to solve the following minimum problem on your own paper. Then, using your final tableau, enter the answer in each relevant box provided below. M inimize : C = 3x 1 + 4x 2 Subject to the following constraints: 2x 1 + x 2 ≥ 2 2x 1 + x 2 ≥ 6 x1 ≥ 0 ; x2 ≥ 0 Minimum value of Value of x1 = Value of x2 = C = https://unlv.instructure.com/courses/102986/quizzes/367207/take 5/9 10/4/21, 1:17 PM Quiz: Section 5.3 Question 8 8 pts Use the simplex method and the Duality Principle to solve the following minimum problem: Minimize: C = 3x 1 + 3x 2 Subject to the constraints: ⎧ 2x 1 + x 2 ≥ 4 ⎪ ⎪ x 1 + 2x 2 ≥ 4 ⎨ x1 ≥ 0 ⎪ ⎩ ⎪ x2 ≥ 0 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. x1 = x2 = C = Question 9 8 pts Use the simplex method and the Duality Principle to solve the following minimum problem: Minimize: C = 2x 1 + 2x 2 Subject to the constraints: ⎧ x 1 + 2x 2 ≥ 3 ⎪ ⎪ 3x 1 + 2x 2 ≥ 5 ⎨ x1 ≥ 0 ⎪ ⎩ ⎪ x2 ≥ 0 https://unlv.instructure.com/courses/102986/quizzes/367207/take 6/9 10/4/21, 1:17 PM Quiz: Section 5.3 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. x1 = x2 = C = Question 10 5 pts The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. ⎡ P y1 y2 s1 ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ 0 0 2 1 0 1 1 0 ⎣ 1 0 −2 0 s2 − RH S ⎤ 1 1 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 3 ⎦ 1 2 1 2 3 2 Find the pivot element(s) in the above tableau, and perform all the necessary pivot operations to obtain the final tableau. Then, using the final tableau, answer the following questions: The minimum function value is: The value of x1 in the minimum problem is : The value of x2 in the minimum problem is: https://unlv.instructure.com/courses/102986/quizzes/367207/take 7/9 10/4/21, 1:17 PM Quiz: Section 5.3 Question 11 5 pts The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. ⎡ P y1 y2 s1 s2 RH S ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ 0 1 −1 1 0 1 0 0 1 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 1 0 −5 ⎣ − 1 1 3 3 3 0 1 3 ⎦ Find the pivot element(s) in the above tableau, and perform all the necessary pivot operations to obtain the final tableau. Then, using the final tableau, answer the following questions: Note: Where applicable, enter fractions in simplified form as 3/5 , 1/2, and so on. The minimum function value is: The value of x1 in the minimum problem is : The value of x2 in the minimum problem is: Question 12 5 pts The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. ⎡ P y1 y2 s1 s2 RH S ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ 0 −2 1 1 0 2 0 9 0 −3 1 0 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎣ 1 −18 0 9 0 18 ⎦ https://unlv.instructure.com/courses/102986/quizzes/367207/take 8/9 10/4/21, 1:17 PM Quiz: Section 5.3 Find the pivot element(s) in the above tableau, and perform all the necessary pivot operations to obtain the final tableau. Then, using the final tableau, answer the following questions: The minimum function value is: The value of x1 in the minimum problem is : The value of x2 in the minimum problem is: Not saved https://unlv.instructure.com/courses/102986/quizzes/367207/take Submit Quiz 9/9