Given the given cost function C(x) = 5300 + 550z + 1.3z and the demand function p(x) = 1650. %3D Find the production level that will maximize profit, to at least 2 decimal places.

If the demand and supply functions for a product are p=800-2q and p=100+0.5q, repectively, find the tax per unit t that will maximize the tax revenue T = t * q.

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.

Suppose the Supply function for a product is given as p=30+ 0.001x^2   and the Demand function is given as  p= 90-0.3x .  Sketch the graph of the two functions, for 0 ≤ x ≤ 300. Make sure to LABEL your x and y axes with their scales. Find the point of intersection between the two functions. You do not need to do this algebraically. Find the Consumer’s Surplus using calculus.

The marginal profit for selling à Bronco souvenir hats is modeled by P'(x) = 7 -0.02x dollars. Suppose your fixed costs are $ 490. First find the number of hats you would like to sell in order to maximize your profit: (This requires remembering some concepts about optimization from Math 30.) Now compute the profit for selling that many units, according to the model.