1. (10") Consider the production problem of n products labeled by j = 1,2,..., n. The unit selling price for the j-th pr

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1 10 Consider The Production Problem Of N Products Labeled By J 1 2 N The Unit Selling Price For The J Th Pr 1 (45.32 KiB) Viewed 74 times

1. (10") Consider the production problem of n products labeled by j = 1,2,..., n. The unit selling price for the j-th product is denoted by Pj. All products can be produced from m raw materials. The production of product j requires any units of raw material i, i = 1,..., m. The i-th raw material can be procured at a unit price . The company has a total budget of B that can be used to procure the raw materials. Naturally, we assume that all the parameters here are nonnegative. The problem is to find the production plan that maximizes the total profit (revenue from selling the products minus the procurement cost). (a) (7') Let x; be the production quantities of product j, j = 1,..., and yi be the procurement quantities of raw material i, i = 1,...,m. (i) Formulate a linear programming model for the problem. (ii) Let 02 Gm denote the bill-of-material matrix and P1 P2 p = -65 --*) 11 22 C1 02 Cm PR an Ym Express your model in matrix form. (b) (3) Formulate a model for the problem without introducing the procurement decisions yi