Solve these problems using graphical linear programming and answer the questions that follow. Use simultaneous equations to determine the optimal values of the decision variables.

a.	Maximize	Z = 4x1 + 3x2
	Subject to

Material	6x1 + 4x2		48	lb
Labor	4x1 + 8x2		80	hour
	x1, x2		0

1. What are the optimal values of the decision variables and Z?

2. Do any constraints have (nonzero) slack? If yes, which one(s) and how much slack does each have?

multiple choice 1

• None of the constraints have any slack. Both constraints are binding.

• The first constraint has a slack of 10.

• The second constraint has a slack of 15.

3. Do any constraints have (nonzero) surplus? If yes, which one(s) and how much surplus does each have? multiple choice 2

• None of the constraints have any surplus.

• The first constraint has a surplus of 15.

• The second constraint has a surplus of 20.

4. Are any constraints redundant? If yes, which one(s)? multiple choice 3

• Yes, the first constraint is redundant.

• Yes, the second constraint is redundant.

• No, there are no redundant constraint.

b.	Maximize	Z = 2x1 + 10x2
	Subject to

Durability	10x1 + 4x2		40	week
Strength	1x1 + 6x2		24	psi
Time	1x1 + 2x2		14	hour
	x1, x2		0

1. What are the optimal values of the decision variables and Z? (Round your answers to 2 decimal places.)

2. Do any constraints have (nonzero) slack? If yes, which one(s) and how much slack does each have?

multiple choice 4

• None of the constraints have any slack.

• The first constraint has a slack of 10.

• The second constraint has a slack of 15.

3. Do any constraints have (nonzero) surplus? If yes, which one(s) and how much surplus does each have? multiple choice 5

• None of the constraints have any surplus.

• The first constraint has a surplus of 20.

• The second constraint has a surplus of 15.

4. Are any constraints redundant? If yes, which one(s)? multiple choice 6

• Yes, the first constraint is redundant.

• Yes, the second constraint is redundant.

• No, there are no redundant constraint.

c.	Maximize	Z = 6A + 3B (revenue)
	Subject to

Material	20A + 6B		600	lb
Machinery	25A + 20B		1,000	hour
Labor	20A + 30B		1,200	hour
	A , B		0

1. What are the optimal values of the decision variables and Z?

2. Do any constraints have (nonzero) slack? If yes, which one(s) and how much slack does each have?

multiple choice 7

• The third constraint has a slack of 120.

• The second constraint has a slack of 60.

• The first constraint has a slack of 80.

3. Do any constraints have (nonzero) surplus? If yes, which one(s) and how much surplus does each have? multiple choice 8

• None of the constraints have any surplus.

• The second constraint has a surplus of 15.

• The first constraint has a surplus of 20.

4. Are any constraints redundant? If yes, which one(s)? multiple choice 9

• Yes, the first constraint is redundant.

• Yes, the second constraint is redundant.

• No, there are no redundant constraint.