Question

Question 1 [35 marks]
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 LINDO 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 changer?

Answer 1

(b) optical plan :

M_{1 = 0}

_{M2 = 220.5882 Kg}

_{M3 = 264.7059 Kg}

_{M4 = 514.7059 Kg}

_{Minimized cost = $5764.706}

© We can see decreased expense is 0.088235294 for scoop type one So the cost needs ton be diminished by 0.088235294 so that Purchasin would get it.

(d) No the buying plan won't change as increment of 0.4 is with in suitable increment limit for scrap Type 2

truly cost of buying metals will Increase by 220.5882*0.4=88023528

(e) expanding roof on the Iron substance by one rate point will give cost decrease of - 10470588235 upto all out 68% of roof of iron requirement

(i.e an expansion of most extreme 18%) so obtaining chief ought not decrease cost by more than - 1.4705882535 for per rate point Increase of roof.