# Quantitative methods

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Missouri Mineral Products (MMP) purchases two unprocessed ores from Bolivia Mining, which it uses in the production of various compounds. Its current needs are for 800 pounds of 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 MMPâ€™s cost per 100 pounds are given in the following table.

Ore Copper Zinc Iron Waste Cost
La Paz ore 20 20 20 40 \$100
Sucre ore 40 25 10 25 \$140
Suppose the objective is to minimize the total purchasing costs, answer the following questions:
a) (20 Points) Write the linear programming model for this problem. Define the variables precisely. (Hint: MMP is deciding how many of each type of ore to buy in order to extract enough minerals to satisfy its customers.)
b) (20 Points) Find the optimal solution using the graphical method. Show all steps. Find the points of intersection algebraically.
c) (10 Points) Find the optimal solution using Excel Solver. Copy and paste the Excel spreadsheet and the Answer Report.
Answer the following two questions using the sensitivity report!
d) (Bonus 5 Points) what happen to the optimal decision and optimal cost if the price for La Paz ore increases to \$110 per 100 pounds?
e) (Bonus 5 Points) what happen to the optimal decision and optimal cost if the demand for iron increased from 500 pounds to 550 pounds?

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