Question 1 [35 marks] A foundry that specializes in producingcustom blended alloys has received an order for 1 000 kg of analloy containing at least 5% chromium and not more than 50% iron.Four types of scrap which can be easily acquired can be blended toproduce the order. The cost and metal characteristics of the fourscrap 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 purchasingmanager 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 scraptype i purchased, i=1,2,3,4. (a) Solve this model using LINDO orSOLVER. (b) Write down the foundry's optimal purchasing plan andcost. 4 PBA4804 OCTOBER/NOVEMBER 2019 PORTFOLIO EXAMINATION [TURNOVER] Based on your LINDO or SOLVER solution answer the followingquestions by using only the initial printout of the optimalsolution. (This means that you may not change the relevantparameters in the model and do reruns.) (c) How good a deal wouldthe purchasing manager need to get on scrap type 1 before he wouldbe willing to buy it for this order? (d) Upon furtherinvestigation, the purchasing manager finds that scrap type 2 isnow being sold at R5,40 per kg. Will the purchasing plan change? Byhow much will the cost of purchasing the metals increase? (e) Thecustomer is willing to raise the ceiling on the iron content inorder to negotiate a reduction in the price he pays for the order.How should the purchasing manager react to this? (f) The customernow specifies that the alloy must contain at least 6% chromium. Canthe purchasing manager comply with this new specification? Will theprice charged for the order change?