Question

1. In planning a restaurant, it is estimated that a profit of $8 per seat will be made if the number of seats is no more than 50, inclusive. On the other hand, the profit on each seat will decrease by $0.10 for each seat above 50 (meaning that for seat number 51, the profit per seat is $7.90, for 52 seats, the profit per seat is $7.80, etc).

(a) What is the function that describes the profit based on the number of seats in the restaurant? (Note: it is a piecewise function)

(b) What are the critical numbers of this function? What other points might we need to test to find a maximum or minimum?

(c) What number of seats produces the maximum profit?

(d) What is the maximum profit?

Answer 1