A firm produces three products A, B, and C, each of which passes through three departments:

Fabrication, Finishing and Packaging. Each unit of product A requires 3, 4 and 2; a unit of product B requires 5, 4 and 4, while each unit of product C requires 2, 4 and 5 hours respectively in the three departments.

Everyday, 60 hours are available in the fabrication department, 72 hours in the finishing department and 100 hours in the packaging department.

The unit contribution of product A is Rs 5, of product Bis Rs 10, and of product C is Rs 8.

Required:

(a) Formulate the problem as an LPP and determine the number of units of each of the products, that should be made each day to maximise the total contribution. Also determine if any capacity would remain unutilised.

(b) If the optimal solution obtained does not require the production of some product, explain as to why such product would not be produced. In this context, indicate the quantity (quantities) of other product/
s that would be foregone for producing such product.

(c) What would be the effect on the solution of each of the following:
(i) obtaining an order for 6 units of product A, which has to be met.
(ii) an increase of 20 percent capacity in the fabrication department.