28. In a product-mix problem, x1, x2, x3, andx4 indicate the units of products A, B, C, andD respectively and we have:

(a) Solve it with simplex method and find out the optimal product-mix as well as the total maximum profit contribution.

(b) Is there any other optimal solution to the problem?

(c) Write the dual to the given LP problem. Obtain the optimal values of the dual variables and verit)'
that the primal and the dual problems have the same objective function values.

(d) What are the shadow prices of the machine hours on the three machines? Ifwe wish to expand the production capacity, which of the three machines should be given priority?
(

e) If a customer is prepared to pay a higher price for the product A, by how much should the price is increased so that the comapanY's profit remains unchanged?
( t) If the profit contribution from product A increases b Y Rs 4 to 5 per unit, will it affect the product mix?

Transcribed Image Text:

Maximise profit Subject to Z=4x+6x2+3x3 + x4 1.5x+2x2 + 4x3 + 3x4 550 (Machine I hours) 4x1 + x2 + 2x3 + x4 700 (Machine II hours) 2x + 3x2 + x3 + 2x4 200 X1, X2, X3, and x 0 (Machine III hours)