A fast-food restaurant determines the cost and revenue models for its hamburgers. C = 0.2x + 7400, 0 < x < 50,000 1 (68,000x – x²), 10,000 0

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
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ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
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Chapter5: Solving Systems Of Linear Equations
Section: Chapter Questions
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A fast-food restaurant determines the cost and revenue models for its hamburgers.
C = 0.2x + 7400,
0 < x < 50,000
1
(68,000x – x²),
10,000
0 <x < 50,000
R =
(a) Write the profit function for this situation.
P =
(b) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answer 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 changes from decreasing to increasing at this value of x, the maximum profit occurs at this value.
Because the function is always increasing, the maximum profit occurs at this value of x.
Transcribed Image Text:A fast-food restaurant determines the cost and revenue models for its hamburgers. C = 0.2x + 7400, 0 < x < 50,000 1 (68,000x – x²), 10,000 0 <x < 50,000 R = (a) Write the profit function for this situation. P = (b) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answer 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 changes from decreasing to increasing at this value of x, the maximum profit occurs at this value. Because the function is always increasing, the maximum profit occurs at this value of x.
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