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 user cost of each thousand bars (in millions of dollars)facing the OZ Mining Company this year. $$\begin{array} { c c c } \begin{array} { c } \text { Quantity of Gold Bars } \ \text { (in thousands) }\ \hline \end{array} & \begin{array} { c } \text { Extraction Cost } \ \text { (in millions of dollars) }\ \hline \end{array} & \begin{array} { c } \text { User Cost } \ \text { (in millions of dollars) }\ \hline \end{array} \ 0 & \$ 10 & \$ 5 \ 1 & 15 & 5 \ 2 & 20 & 5 \ 3 & 25 & 5 \ 4 & 30 & 5 \ 5 & 35 & 5 \end{array}$$ Refer to the data.Suppose that a new government regulation is going to shut down OZ's mining operation one year from now.If the current price per bar of gold is $25,000,how many bars (in thousands)should OZ extract and sell this year?

Question

Quizplus · Accepted Answer

Given the current price per bar is $25,000, and each quantity represents thousands of bars, the revenue from selling each thousand bars is $25 million. The total cost (extraction cost + user cost) for each quantity level is $15M, $20M, $25M, $30M, $35M, and $40M respectively. The profit for each level can be calculated by subtracting the total cost from the revenue ($25M). The profit turns negative after extracting 3 thousand bars, making 3 the optimal quantity to extract and sell.

The Table Below Shows the Quantity of Gold Bars (Qb)in

The Table Below Shows the Quantity of Gold Bars (Q_b)in