Q5 to Q10 are based on this problem.

Jack could manufacture COVID 19 test kits using two processes. For process 1, the unit cost of the first two million kits is $10, and the unit cost is reduced to $4 afterward. For process 2, the unit cost of the first five million kits is $8, and the unit cost is reduced to $5 after that. Jack has a budget of 20 million dollars and likes to maximize the number of test kits. Formulate this problem as an IP. I suggest you write out the complete formulation before you answer the multiple-choice questions.

Decision Variable:

X11: millions of kits manufactured at $10 using process 1

X21: millions of kits manufactured at $4 using process 1

X12: millions of kits manufactured at $8 using process 2

X22: millions of kits manufactured at $5 using process 2

Question 5

What is the objective function?

Group of answer choices

A. Max X11+X21+X12+X22

B. Min X11+X21+X12+X22

C. Max 10X11+4X21+8X12+5X22

D. Min 10X11+4X21+8X12+5X22

Question 6

We need a binary variable Y1 to ensure that before we can manufacture the test kits at the reduced cost of $4 using process 1, at least two million test kits have been manufactured using process 1. How you define Y1?

Group of answer choices

A. Y1=1 if X21 positive; 0 otherwise

B. Y1=1 if X11 positive; 0 otherwise

C. Y1=1 if X12 positive; 0 otherwise

D. Y1=1 if X22 positive; 0 otherwise

Question 7

X21-M1Y1<=0, where M1 is a large enough number. Which of the following statement regarding this constraint is not true?

Group of answer choices

A. This constraint ensures Y1 =1 when X21 is positive; 0 otherwise. The logic is similar to the production setup constraint.

B. M1=5 is large enough.

C. M1 is large enough if it is larger than the largest possible value of X21.

D. This constraint ensures at least two million test kits are manufactured using process 1.

Question 8

Which two constraints ensure the economies of scale in Process 2 is properly formulated?

Group of answer choices

A. X12-5Y2>=0; X22-5Y2<=0

B. X12-5Y1>=0; X22-5Y2<=0

C. X22-5Y2>=0; X12-5Y2<=0

D. X22-5Y1<=0; X12-5Y2<=0

Question 9

What are the optimal solution and optimal objective function value?

Group of answer choices

A. Jack should produce 2.5 million test kits using process 2 and the total number of test kits is 2.5 million.

B. Jack should produce 2.5 million test kits using process 1 and the total number of test kits is 2.5 million.

C. Jack should produce 2 million test kits using process 1 and the total number of test kits is 2 million.

D. Jack should produce 2 million test kits using process 2 and the total number of test kits is 2 million.

Question 10

You lose the Sensitivity Analysis Report when you incorporate integer constraints in your formulation. But you can still revise your formulation and resolve the IP to perform some scenario analysis. Which of the following statement regarding the effect of the increased budget is not true? Hint: When the budget is increased, M1 and M2 need to be larger to be large enough.

Group of answer choices

A. If the budget is increased from 20 million to 40 million, we get more than 2.5 million more test kits because of the economies of scale.

B. If the budget is 40 million instead of 20 million, we will use process 1 to produce 7 million test kits.

C. If the budget is 60 million instead of 20 million, we will use process 1 to produce 12 million test kits.

D. If the budget is 60 million instead of 20 million, we will use both processes 1 and 2 to produce 12 million test kits.