The demand function for a new laptop is p(x) = -3x + 40 where p(x) represents the selling price, in hundreds of dollars, and x is the number of laptops sold, in hundreds. The cost function is C(x) = 16x + 20. a. Determine the profit function. b. Calculate the maximum possible profit.

A ceramics store manufactures and sells coffee mugs. The revenue r(x) from the sale of x coffee mugs is given by r(x)=6.5x. Suppose the function for the cost of manufacturing x coffee mugs is c(x)=0.75x+1850. a. Write the profit function. b. Find the profit on 500,1000, and 5000 coffee mugs.

A contractor purchases a backhoe for $37, 300. Fuel and standard maintenance cost $5.95 per hour, and the operator is paid $12.03 per hour. a. Write a cost function for the cost C(z) of operating the backhoe for hours. Be sure to include the purchase price in the cost function. Cost function: C(z) = dollars b. If customers pay $27.77 per hour for the contractor's backhoe service, write the revenue function R(z) for the amount of revenue gained from a hours of use. Revenue function: R(x) = I c. Write the profit function P(x) for the amount of profit gained from a hours of use. Profit function: P(x) = dollars dollars d. How many hours must the backhoe be used in order to break even (assume that part of an hour counts as a whole hour)? In order for the contractor to break even, customers need to pay to use the backhoe for a total of hours.

Imani is opening an online shop to sell her handmade candles. She has determined that her initial start-up costs will be $110, and it will cost her $6 to produce each candle. Imani plans to sell each candle for $22. Let x be the number of candles. Write the revenue function, R(x), for selling the candles. Answer R(x) = Keypad Keyboard Shortcuts