The manager of FYZ Incorporated has been presented with the following LP model:
ID: 470267 • Letter: T
Question
The manager of FYZ Incorporated has been presented with the following LP model:
Minimize (costs) ?Z = 30A + 45B
?
?Subject to?5A + 2B > 100
?4A + 8B > 240
? B > 20
? ?A and B > 0
?She would like your assistance with several questions below.
a.) What is the proper name of the last constraint shown in the model?
b.) What is the optimal value of the objective function?
c.) What are the optimal values of the two decision variables?
d.) If the cost of B could be reduced to $42 per unit, how many units of B would be optimal?
e.) If the cost of B could be reduced to $42 per unit, what would the minimum total cost be?
f.) What is the dual value (AKA--shadow price) for the RHS value of the first constraint?
g.) What is the range of feasibility for the RHS value of the first constraint?
h.) By what amount would the total cost change, and in what direction, if the RHS value of the first constraint was changed to 110? Please explain the rationale for your answer.
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Explanation / Answer
Minimize Z = 30A + 45B
S.T 5A +2B > 100
4A + 8B > 240
B > 20
A, B > 0
a) What is the proper name of the last constraint shown in the model ?
They are called "Non-negative" constraints
c) What is the optimal value of the two decision variables?
5A + 2B > 100
4A + 8B > 240
Consider inserting all the values in the equation, the values that best satisfies both the equations are (10,25)
5(10) + 2(25) > 100
50 + 50 = 100
4(10) + 8(25) > 240
40 + 200 = 240
b) What is the optimal value of the objective function
Z = 30A + 45B
= 30(10) + 45(25)
= 1350
d) If the cost of B would reduce to $42 per unit, how many units of B would be optimal?
25 units of B would be optimal.
e) If the cost of B could be reduced to $42 per unit, what would be minimum total cost be?
Z = 30A + 42B
= 30 (10) + 42 (25)
= 1350
f) What is the dual value for the RHS value of the first constraint?
The shadow price for the RHS value of the first constraint is 100
g) What is the range of feasibility for the RHS value of the first constraint?
For the first constraint, 5A + 2B > 100 the range of feasibility for RHS value is towards outside.
So the range of feasibility is from 100 to infinity
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