A contractor purchases a backhoe for $37000. Fuel and standard maintenance cost

Question

A contractor purchases a backhoe for $37000. Fuel and standard maintenance cost $6.42 per hour, and the operator is paid $12.66 per hour. a. Write a cost function for the cost C of operating the backhoe for x hours. Be sure to include the purchase price in the cost function. Cost equation: C = 37000+19.08x dollars b. If customers pay $33.07 per hour for the contractor's backhoe service, write the revenue function R for the amount of revenue gained from x hours of use. Revenue equation: R = 33.07x dollars c. Write the profit function P for the amount of profit gained from x hours of use. Profit equation: P = 33.07x-37000+19.08x dollars d. Use part c. to find the number of hours the backhoe must be used to break even (when Profit = 0). Please make sure your answer is correct to at least the nearest whole number. Break even = hours.

Explanation / Answer

We have C=37000+19.08x

R=33.07x

P=33.07x-37000-19.08x

When P=0

13.99x=37000

x=2644.75 hours

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