MAT 1300 Study Guide - Fixed Cost

The demand for a certain type of cosmetic is given by p- 360 -x where p is the price in dollars when x units are demanded (a) Find the revenue Rx) that would be obtained at a price p (Hint Revenue Demand x Price) (b) Graph the revenue function R(x) (c) Find the price that will produce maximum revenue d) What is the maximum revenue?

2. A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x rackets/day is given by C(x) 400+4x+ 0.0001x2. Each racket can be sold at a price of p dollars, where p is related to x by the demand equation p = 10-0.0004x. If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer. What is the maximum profit? (4 pts) 3. Suppose the total cost function for manufacturing a certain product is C(x) = 0.002x' + 24 dollars, where x represents the number of units produced. Find nduction that will minimize the average cost C'(x).(4 pts) ounl ef er

9. (22 pts) The cost, in dollars, for a company to produce x doodads is given by C(x) 500 7x for x 20, and the price-demand function, in dollars per doodads, is p(x) 17-.010x for 0 sx s 1700. Find the following. SHOW YOUR WORK Hint: Your numbers will be "nice" if done correctly. (a) Write the equation for the profit function Pa). Graph the profit function below. (b) Find the vertex of the profit function P(x) using algebra. Show algebraic work. (e) State the maximum profit and the number of doodads which yield that maximun profit: The maximum profit is when doodads are produced and sold (d) Determine the price to charge per doodad in order to maximize profit. (e) Find and interpret the break-even points Activity Details