Question

A manufacturer is marketing a product made of an alloy material requiring a certain specified composition. The three critical ingredients of the alloy are manganese, silicon and copper. The specifications require 15 pounds of manganese, 22 pounds of silica and 39 pounds of copper for each ton of alloy to be produced. This mix ingredients require the manufacturer to obtain inputs from three different mining suppliers. Ore from the different suppliers has different concentrations of alloy ingredients, as detailed on the Table below:

	Supplier 1 (lb/ton of ore	Supplier 2 (lb/ton of ore)	Supplier 3 (lb/ton of ore)
Manganese	1	3	2
Silicon	2	4	3
Copper	3	4	7

Given this information, the supplier must determine how much ore to purchase from each supplier so that there is no waste of the alloy ingredients. A solution to the problem can be found by defining the following variables:

X_j = amount of ore purchased from supplier j

C_i = amount of ingredient i required per ton of alloy

A_ij = amount of ingredient i contained in each ton of ore shipped from supplier j

What amount of ore should be purchased from each supplier?

Answer 1