Question

A foundry that specializes in producing custom blended alloys has received an order for 1 000 kg of an alloy containing at least 5% chromium and not more than 50% iron. Four types of scrap which can be easily acquired can be blended to produce the order. The cost and metal characteristics of the four scrap types are given below: Scrap type Item 1 2 3 4 Chromium 5% 4% - 8% Iron 40% 80% 60% 32% Cost per kg R6 R5 R4 R7 The purchasing manager has formulated the following LP model: Minimise COST = 6M1 + 5M2 + 4M3 + 7M4 subject to 0,05M1 + 0,04M2 + 0,08M4 ≥ 50 (CHRM) 0,40M1 + 0,80M2 + 0,60M3 + 0,32M4 ≤ 500 (IRON) M1 + M2 + M3 + M4 = 1000 (MASS) and all variables ≥ 0, where Mi = number of kg of scrap type i purchased, i=1,2,3,4. (a) Solve this model using LINGO or SOLVER. (b) Write down the foundry's optimal purchasing plan and cost. Based on your LINDO or SOLVER solution answer the following questions by using only the initial printout of the optimal solution. (This means that you may not change the relevant parameters in the model and do reruns.) (c) How good a deal would the purchasing manager need to get on scrap type 1 before he would be willing to buy it for this order? (d) Upon further investigation, the purchasing manager finds that scrap type 2 is now being sold at R5,40 per kg. Will the purchasing plan change? By how much will the cost of purchasing the metals increase? (e) The customer is willing to raise the ceiling on the iron content in order to negotiate a reduction in the price he pays for the order. How should the purchasing manager react to this? (f) The customer now specifies that the alloy must contain at least 6% chromium. Can the purchasing manager comply with this new specification? Will the price charged for the order change?

Answer 1

Sol:- (a) The output using SOLVER

(b)

Formula:-

Sensitivity Report