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# For numbers 35-40, Please refer to the following problem: Axis is...

For numbers 35-40, Please refer to the following problem: Axis is an aspiring freshman at Saint Louis University. He realizes that "all study and no play make Axis a dull boy." As a result, Axis wants to apportion his available time of about 10 hours a day between study and play. He estimates that play is twice as much fun as study. He also wants to study at least as much as he plays. However, Axis realizes that if he is going to get all his homework done, he cannot play more than 4 hours a day. With the use of Linear Programming (LP), help Axis allocate his time to maximize his pleasure from both study and play.

35. Which of the following is the most appropriate representation for variables 𝑥, 𝑦, and 𝑧 for this problem?

A. 𝑥 represents the degree of pleasure from study 𝑦 represents the degree of pleasure from play 𝑧 represents the degree of pleasure from both study and play

B. 𝑥 represents the degree of pleasure from study 𝑦 represents the degree of pleasure from play 𝑧 represents the total number of hours for both study and play

C. 𝑥 represents the number of hours per day allocated for study 𝑦 represents the number of hours per day allocated for play 𝑧 represents the total number of hours for both study and play

D. 𝑥 represents the number of hours per day allocated for study 𝑦 represents the number of hours per day allocated for play 𝑧 represents the degree of pleasure from both study and play

36. What should be the corresponding objective function for the LP model in this problem?

A. 𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑧 = 2𝑥 + 𝑦

B. 𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑧 = 𝑥 + 2𝑦

C. Minimize 𝑧 = 𝑥 + 2𝑦

D. Minimize 𝑧 = 2𝑥 + 𝑦

37. Which of the following is the complete set of constraints for the LP model in this problem?

A. 𝑥 + 𝑦 ≤ 10 𝑥 ≥ 𝑦 𝑦 ≤ 4 𝑥, 𝑦 ≥ 0

B. 𝑥 + 𝑦 ≤ 10 𝑥 ≥ 𝑦 𝑦 ≤ 4 𝑥, 𝑦 ≤ 0

C. 𝑥 + 𝑦 ≤ 10 𝑥 ≤ 𝑦 𝑦 ≤ 4 𝑥, 𝑦 ≥ 0

D. 𝑥 + 𝑦 ≤ 10 𝑥 ≤ 𝑦 𝑦 ≤ 4 𝑥, 𝑦 ≤ 0

38. How many corner points are there in this LP problem?

A. 1

B. 2

C. 3

D. 4

39. Which of the following corner points provides the optimal solution for this LP problem?

A. (0,0)

B. (4,4)

C. (6,4)

D. (10,0)

40. Which of the following is the optimal value of the objective function for the LP model in this problem?

A. 0

B. 14

C. 16

D. 20

41. Which of the following is referred to as a graph where each of the vertices is connected by an edge to all other vertices of a graph?

A. Complete Graph

B. Connected Graph

C. Regular Graph

D. Simple Graph

with a complete solution please, thankyou.

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