Question

Decision Variables	S
	T
Minimize	1.8S + 2.20T
Subject to:
Potassium	5S + 8T >=	200	gr
Carbohydrate	15S + 6T >=	240	gr
Protein	4S + 12T >=	180	gr
T	T >=	10	gr
	S, T >=	0

Please provide "Solver"informations.

1. What are the optimal values of the decisions variables when minimizing production costs?

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

3. Do any of the constraint have surplus? If yes, which one(s) and how much surplus does each have?

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

Answer 1

We solve the given problem using Excel solver as shown below:

The above solution in the form of formulas along with Excel Solver extract is shown below for better understanding and reference:

Based on the above, we answer the question as shown below:

1) The optimal values are:

S = 8

T = 20

2) No. There are no constraints that have slack. Slack = Right-hand side - Left-hand side. Since RHS <= LHS in all constraints, there is no slack.

3) Yes, The constraints with Surplus are:

Protein and for T

The surplus for Protein = LHS - RHS = 272 - 180 = 92

Surplus for T = LHS - RHS = 20 - 10 = 10

The redundant constraint can be those which have Surplus. Hence, we delete the constraint for Protein and solve the LPP in Excel Solver to check if there is any change in Optimal solution.

There is no change in the Optimal solution. Hence, the constraint for protein is redundant.

We now delete constraint for T.

There is no change in the Optimal solution. Hence, the constraint for T is redundant.

Answer: There are 2 redundant constraints. The constraint for Protein and constraint for T.

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