A manufacturer is marketing a product made of an alloy materialrequiring a certain specified composition. The three criticalingredients of the alloy are manganese, silicon and copper. Thespecifications require 15 pounds of manganese, 22 pounds of silicaand 39 pounds of copper for each ton of alloy to be produced. Thismix ingredients require the manufacturer to obtain inputs fromthree different mining suppliers. Ore from the different suppliershas different concentrations of alloy ingredients, as detailed onthe 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 oreto purchase from each supplier so that there is no waste of thealloy ingredients. A solution to the problem can be found bydefining the following variables:
Xj = amount of ore purchased from supplier j
Ci = amount of ingredient i required per ton ofalloy
Aij = amount of ingredient i contained in each ton ofore shipped from supplier j
What amount of ore should be purchased from each supplier?
