Exam 10: Further Applications of the Derivative

If the total revenue function for a blender is $R ( x ) = 35 x - 0.25 x ^ { 2 },$ determine how many units x must be sold to provide the maximum total revenue in dollars.

Average costs. Suppose the average costs of a mining operation depend on the number of machines used, and average costs, in dollars, are given by $\bar { C } ( x ) = 5 x + \frac { 4500 } { x } , \quad x > 0$ , where x is the number of machines used. What is the minimum average cost?

If the total cost function for a product is $C ( x ) = 500 + 3 x + 0.08 x ^ { 2 }$ dollars, determine how many units x should be produced to minimize the average cost per unit?