For Each Carload of Ore Removed from the Matchless Mine

question 3

Multiple Choice

For each carload of ore removed from the Matchless Mine, 1 pound of lead and 1 ounce of silver is smelted. The cost of mining and processing 1 carload of ore is C(Q) = 400 + 2Q + 0.04Q². The demand for silver (per ounce) is P_s = 30 - 0.30Q_s and the demand for lead (per pound) is P_l = 6 - 0.02Q_l. What should the owners of the Matchless Mine do to maximize profits (in the long run) ?

• A) Mine and process 47.22 carloads of ore, sell 47.22 ounces of silver, and sell 47.22 pounds of lead.
• B) Mine and process 50 carloads of ore, sell 50 ounces of silver, and sell 33.33 pounds of lead.
• C) Mine and process 150 carloads of ore, sell 41.18 ounces of silver, and sell 150 pounds of lead.
• D) Mine and process 150 carloads of ore, sell 50 ounces of silver, and sell 150 pounds of lead.
• E) Shut down the mine.

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Definitions:

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