22. A manufacturing company makes three products, each of which requires three operations as part of the manufacturing process. The company can sell all of the products it can manufacture but its production capability is limited by the capacity of its operations centres. Additional data concerning the company are as follows:

(a) What is the optimal product-mix? What is the maximum profit?

(b) What are the shadow prices of the resources? When the optimal solution has been reached, which resource has the highest marginal value?
(

c) Over what range in each of the RHS values, are these shadow prices valid?
(

d) What are the ranges over which the objective function co-efficients can vary for each of the two decision variables?

(e) State the dual to this problem and write its solution.

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Product Manufacturing requirement (hours/unit) Cost Selling price (Rs) (Rs) Centre 1 Centre 2 Centre 3 ABC 1 3 3 4 2 2 Hours available 160 120 80 =20 2128 15 20 10 526 16