Economists who study production of goods by a firm consider two functions. The revenue function is the revenue the firm receives when x number of units are sold. The cost function is the cost the firm incurs when producing x number of units. The derivatives of these functions and are called by economists the marginal revenue and cost function. The figure shows graphs of the marginal revenue function and the marginal cost function for a manufacturer. Assume that and are measured in thousands of dollars.

(a) What does the shaded area in the figure represent?

(b) Upon closer inspection of the graph, a table of data values for and (each in thousands of dollars per unit manufactured) is generated below:

Use the Midpoint Rule with to estimate the value of the shaded region (in thousands of dollars).

Value of the shaded region = thousand dollars

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