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

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Basic Math

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

Afast-food restaurant determines the cost and revenue models for itshamburgers.
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 isincreasing and decreasing. (Enter your answers using intervalnotation.)

increasing    
decreasing    



(c) Determine how many hamburgers the restaurant needs to sell toobtain a maximum profit.
hamburgers

Explain your reasoning.

Because the function is always decreasing, the maximum profitoccurs at this value of x.Because the function changesfrom increasing to decreasing at this value of x, themaximum profit occurs at thisvalue.     The restaurant makes the sameamount of money no matter how many hamburgers are sold.Because thefunction is always increasing, the maximum profit occurs at thisvalue of x.Because the function changes from decreasing toincreasing at this value of x, the maximum profit occursat this value.

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