Suppose a product's revenue function is given by R(q) = -3q² +800q, where R(q) is in dollars and qis units sold. Also, it's cost function is given by C(q) = 34q+26667, where C(q) is in dollars and q is units produced. Find a simplified expression for the item's Marginal Profit function (P'(aq)) and record your answer in the box. Be sure to use the correct variable. (Use the Preview button to check your syntax before submitting your final result). Answer: P'(q)

A company's cost (in dollars) to produce x units is C(x) = 82 + 6x -0.04x^2. Find the marginal cost when 25 units are sold. Round to the nearest cent, and do not enter the dollars sign.

Assume that it costs a company approximately C(x) = 400,000 + 120x + 0.002x? dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is ---Select--- O than the average cost from (b). This means that the average cost is ---Select--- O at a production level of 10,000 smartphones.