Question

1.

In an alternate universe, Warren Buffet decides to revive Circuit City, which produces product A and product B. Each product needs to go through two processes. Each instance of product A produced requires 4 hours in the first process and 2 hours in the second process. Each instance of product B produced requires 3 hours in the first process and 4 hours in the second process. There are 150 hours of capacity available each week in each process. Each unit of product A yields $9.00 in profit for Circuit City, and each unit of product B yields $6.00 in profit. If Circuit City produces 30 units of A and 10 units of B, the amount of slack (in hours) for the second process is ________.

Group of answer choices

50 hours

30 hours

20 hours

40 hours

2.

The point ________ is feasible for the constraint 2x₁ + 6x₂ ≤ 25.

Group of answer choices

(x1 = 3, x2 = 4)

(x1 = 1, x2 = 4)

(x1 = 3, x2 = 3)

(x1 = 5, x2 = 3)

Answer 1

Q1 : 50 hours

We know that each unit of A uses 2 hours of second process and each unit of B uses 4 hours of second process. If 30 units of product A and 10 units of product B are produced, total hours used of second process are 30*2+10*4 = 60+40 = 100. As there are 150 hours of second process, slack for second process is 150-100 = 50 hours

Q2 : x1 = 3, x2 = 3

To find the point which is feasibke for the constraint 2x1+6x2  ≤ 25, we need to substitute each of the given points and check which points satisfy the given constraint

(x1 = 3, x2 = 4) : 2*3+6*4 = 6+24 = 30. This is not less than 25. Hence this is not the correct answer.

(x1 = 1, x2 = 4) : 2*1+6*4 = 2+24 = 26. This is not less than 25. Hence this is not the correct answer.

(x1 = 3, x2 = 3) : 2*3+6*3 = 6+18 = 324. This is less than 25. Hence this is the correct answer.

(x1 = 5, x2 = 3) : 2*5+6*3 = 10+18 = 28. This is not less than 25. Hence this is not the correct answer.