Problem 19-2 (Static)

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

a.	Minimize	Z = 1.80S + 2.20T
	Subject to:

Potassium	5S + 8T		200	grams
Carbohydrate	15S + 6T		240	grams
Protein	4S + 12T		180	grams
T	T		10	grams
	S,T		0

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

S:

T:

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.

• 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

• The third and fourth constraints have surpluses of 92 grams and 10 grams respectively.

• The first and third constraints have surpluses of 90 grams and 10 grams respectively.

• The fourth and first constraints have surpluses of 94 grams and 20 grams respectively.

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

• Yes, the third constraint is redundant.

• Yes, the second constraint is redundant.

• Yes, the first constraint is redundant.

b.	Minimize	Z = 2x1 + 3x2
	Subject to:

D	4x1 + 2x2		20
E	2x1 + 6x2		18
F	1x1 + 2x2		12
	x1, x2		0

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

X1:

X2:

Z:

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

multiple choice 4

• Yes, the constraint F has a slack of 4.6.

• Yes, the constraint E has a slack of 3.6.

• Yes, the constraint D has a slack of 4.2.

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

• No, there is no 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

• No