The table below shows the quantity of gold bars (Q_b) in thousands,the extraction cost for each thousand bars (in millions of dollars) ,and the user cost of each thousand bars (in millions of dollars) facing the OZ Mining Company this year. $$\begin{array}{ccc}\begin{array}{c}\text{ Quantity of Gold Bars }\\ \text{ (in thousands) }\end{array}& \begin{array}{c}\text{ Extraction Cost }\\ \text{ (in millions of dollars) }\end{array}& \begin{array}{c}\text{ User Cost }\\ \text{ (in millions of dollars) }\end{array}\\ 0& \$10& \$5\\ 1& 15& 5\\ 2& 20& 5\\ 3& 25& 5\\ 4& 30& 5\\ 5& 35& 5\end{array}$$ Refer to the data.If the price of a bar of gold is $30,000 this year,how many bars (in thousands) should OZ extract and sell?

A) 2.
B) 3.
C) 4.
D) 5.

To determine the optimal quantity of gold bars to extract and sell, we need to compare the total cost (extraction cost + user cost) for each quantity with the total revenue from selling that quantity at $30,000 per bar. The total cost for each quantity is the sum of the extraction cost and the user cost for that quantity. The revenue is the price per bar ($30,000) times the quantity of bars (in thousands). The company should extract and sell the quantity where the total revenue is greater than or equal to the total cost but becomes less if more bars are extracted. For 3,000 bars, the total cost is $25 million (extraction) + $5 million (user cost) = $30 million, and the revenue is 3,000 bars * $30,000/bar = $90 million. For 4,000 bars, the total cost is $30 million (extraction) + $5 million (user cost) = $35 million, which is less than the revenue of 4,000 bars * $30,000/bar = $120 million. However, the decision is based on maximizing profit while considering the increase in costs. At 3,000 bars, the profit is maximized before the costs increase disproportionately to the revenue.