Problem:
Colorado Gem and Mineral Co. (CGM) purchases two unprocessed ores from Philippines Mining, which it uses in the production of various compounds. Its current needs are for 800 pounds copper, 600 pounds of zinc, and 500 pounds of iron. The amount of each mineral found in each 100 pounds of the unprocessed ores and CGM's cost per 100 pounds are given in the following table.
|
Ore
|
Copper per 100 pounds
|
Zinc per 100 pounds
|
Iron per 100 pounds
|
Waste per 100 pounds
|
Cost per 100 pounds
|
|
Manila ore
|
20
|
20
|
20
|
40
|
$100
|
|
Sucre ore
|
40
|
25
|
10
|
25
|
$140
|
The objective is to determine the amount of each ore that should be purchased in order to minimize the total purchasing cost.
a) Formulate the linear programming model for the problem.
b) Use the Graphical method to find the optimal solution. Show all steps.
c) Use Excel Solver to find the optimal solution. Copy and paste your spreadsheet and the Answer report from Excel.