Hi there, I have the following question:
For a certain manufacturing process a manufacturer requires 1000kg of nickel and 1600kg of tin. He obtains this by buying scrap metal and scrap cars. One tonne of scrap metal yields 100kg of nickel and 400kg of tin, while one tonne of scrap cars yields 100kg of nickel and 100kg of tin. If the scrap metal costs £15 per tonne and scrap cars £5 per tonne, how many tonnes of each should he buy and what will be his capital outlay?
I have only been given one example of linear programming in class, but its for working out maximum profit. This question is a bit different, I can't work out how to arrange it to solve it. Im guessing here I am required to work out the minimum cost that achieves at least the required amount of nickel and tin.
So would I be right in saying the following;
if Nickel = xA and Tin = xB
Minimise 1000xA + 1600xB
Subject to: 100xA + 400xB = 15
and 100xA + 100xB = 5
So xB = 1/30 or 0.0333
and xA = 1/60 or 0.016666
Please could someone confirm that I am on the right track
Many thanks
Jackie