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.

Question

Quizplus · Accepted Answer

To maximize profits, the mine should operate where marginal revenue equals marginal cost. The given functions for cost, demand for silver, and demand for lead allow for the calculation of optimal production levels. The correct choice involves mining and processing an amount of ore where the revenue from selling both silver and lead minus the cost of mining and processing is maximized. This involves solving for Q in the given equations, taking into account the price and cost structures provided.

For Each Carload of Ore Removed from the Matchless Mine