Question

1. A wholesale company has nine storage depots which it proposes to rationalize. Four depots, Q, R, S, and T are to be expanded and five depots, A, B, C, D, and E are to be closed. Thirty six of the mechanical loaders in the depots to be closed will be required for use in the enlarge depots.

The mechanical loaders in the five depots to be closed are: ?: 5, ?: 7, ?: 11, ?: 8, and ?: 9 The additional loaders required at the depots to be expanded are: ?: 8, ?: 9, ?: 11, and ?:8.

The cost of transporting one mechanical loader, in hundreds of cedis, between depots is given below.

Depots to be Depots to be expanded closed

QRST A3379 B6533 C6487 D5454 E4365

a) Show by calculation the minimum cost plan for meeting the rationalization requirement by transfers between depots.

b) State at which depot there will be surplus loaders.

c) State with reasons whether or not your solution is unique.

2. Consider the LP problem below: Minimize: ? = −2? + 8? Subject to:

3? + 4? ≤ 80 −3? + 4? ≥ 8 ? + 4? ≥ 40

a) Solve the above problem using the simplex method of solution.

b) Comment on the nature of solution to the above problem and hence, interpret your results

Answer 1

Doubt in this then comment below.. i will help you..

By rules and regulations we are allow to do only one question at a time...so i do only 2nd..

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please thumbs up for this solution....thanks.

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b) ..

here , in this problem we get an optimal solution.

​​​​​​ And first variable is 0 and 2nd variable value is 20 in optimal splution..

also only one constraints are active and other two are not active...

by taking dual value of constraints , we see that if we increase the RHS of 1st constraints , then maximum value improved...