Question 5. (20 points) OPTIMAL PRODUCT MIX AND WHAT-IF QUESTIONS Consider the problem in Question 4: The AU Mines Company own two mines, X and Y, that produce an ore which, after being crushed, is graded into three classes: high, medium and low- grade. The AU Mines have different operating characteristics as detailed below: Production (Tons/Day) Mine High Medium Low X 6 3 4 Y 1 1 6 Table-Q5-1. Production output of each mine. Additional information has become available about the market for the products. The company has the option the sell the high, medium, low-grade ores extracted from any of the sites to other manufacturers other than the smelting plant. However, the unit revenue ($/ton) earned from the contract with smelting plant is higher than what the other manufacturers will pay. The revenues are provided below. Product type High grade Revenue ($/ton) when $10 Medium grade $12 Low grade $8 sold to the smelting plant Revenue ($/ton) when $10 $9 $7 sold in the market to other manufacturers Table Q5-2. Revenue per ton from different customers The demand of the smelting plant must be met exactly because of the contract. The demand for other manufacturers is higher than the company's production capacity. The company has the market power to determine the amount of products to sell to other manufacturers (and can chose to not sell at all). The demand information is provided below. + Product type High grade Medium grade Low grade Demand of 12 tons/week 8 tons/week 24 tons/week smelting plant unlimited unlimited Demand from unlimited other manufacturers Table Q5-3. Demand from different customers Demand fulfillment Must be met exactly Optional