A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below.

	Hours required by
Operation	A	B	Hours
Cutting	3	4	48
Welding	2	1	36

The decision variables are defined as:

xi = the amount of product i produced

yi = 1 if xi > 0 and 0 if xi = 0

A spreadsheet implementation of the problem is shown below.

Q1. What is the objective function for this problem?

a. Maximize: 17x ₁ + 21x ₂ - 60y ¹ - 80y ₂

b. Minimize: 60y ₁ + 80y ₂

c. Minimize: 17x ₁ + 21x ₂ - 60y ₁ - 80y ₂

d. Maximize: 17x ₁ + 21x ₂

Q2. What is the appropriate formula to use in cell E8 of the Excel implementation of the ILP model for this problem?

a. =SUMPRODUCT(B8:C8,B14:C14) - SUMPRODUCT(B5:C5,B7:C7)

b. =SUMPRODUCT(B5:C5,B7:C7) - SUMPRODUCT(B8:C8,B14:C14)

c. =SUMPRODUCT(B5:C5,B7:C7) - SUMPRODUCT(B8:C8,B15:C15)

d. =SUMPRODUCT(B5:C5,B7:C7) - B8:C8

Q3. Which of the following algebraic constraints creates the link between setting up to produce A's and making some A's for this problem?

a. x ₁ - 18 y ₁ > 0

b. x ₁ - y ₁ = 0

c. = if(x ₁ > 0, y ₁ = 1, y ₁ = 0)

d. x ₁ 1

Transcribed Image Text:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A Number to produce Unit profit Fixed cost Resources Cutting Welding Binary variables Linking constraints 17 B Product A Product B 60 Fixed charge problem 21 80 Hours required 3 4 2 1 D Used E Total profit: Available 48 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A Number to produce Unit profit Fixed cost Resources Cutting Welding Binary variables Linking constraints 17 B Product A Product B 60 Fixed charge problem 21 80 Hours required 3 4 2 1 D Used E Total profit: Available 48 36

Answer rating: 100% (QA)

1 a Maximize 17 x1 ... View the full answer