Question

A fast-food restaurant determines the cost and revenue models for its hamburgers.

A fast-food restaurant determines the cost and revenue models for its hamburgers. C = 0.8x + 7100,     0 ≤ x ≤ 50,000 R = 1 10,000 (66,000x − x2),     0 ≤ x ≤ 50,000 (a) Write the profit function for this situation. P =   (b) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answers using interval notation.) increasing     decreasing     (c) Determine how many hamburgers the restaurant needs to sell to obtain a maximum profit. hamburgers Explain your reasoning. Because the function is always decreasing, the maximum profit occurs at this value of x.Because the function changes from increasing to decreasing at this value of x, the maximum profit occurs at this value.     The restaurant makes the same amount of money no matter how many hamburgers are sold.Because the function is always increasing, the maximum profit occurs at this value of x.Because the function changes from decreasing to increasing at this value of x, the maximum profit occurs at this value.

Answer 1

we have

the profit function,

P' = 0 for the critical point,

now the behavior of P'

	0<P<29000	P=29000	29000<P<50000
sign	+	0	-
behavior	increasing	maximum	decreasing

the interval of increasing,

the interval of decreasing,

the maximum profit at x = 29000 is,

the maximum profit at x = 29000 is 77000