A company makes solar panels. The company’s revenue function, in dollars, is R(n)=10n , where n is the number of panels produced. The cost function is C(n)=100(2)π/30 . R and C are shown on the graph below. a) Estimate from the graph i) the break-even points ii) the number of panels that should be produced for maximum profit b) Write the equation for the profit function P. c) Graph P. d) Use your graph of P to estimate the number of panels that give maximum profit. e) How would your answers for break-even points and maximum profit change if i) the number of dollars of revenue per panel is increased slightly? ii) the cost function is C(n)=100(2)π/35 changed to ? f) What does the number that was changed in part e) ii) represent?
A company makes solar panels. The company’s revenue function, in dollars, is R(n)=10n , where n is the number of panels produced. The cost function is C(n)=100(2)π/30 . R and C are shown on the graph below. a) Estimate from the graph i) the break-even points ii) the number of panels that should be produced for maximum profit b) Write the equation for the profit function P. c) Graph P. d) Use your graph of P to estimate the number of panels that give maximum profit. e) How would your answers for break-even points and maximum profit change if i) the number of dollars of revenue per panel is increased slightly? ii) the cost function is C(n)=100(2)π/35 changed to ? f) What does the number that was changed in part e) ii) represent?
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.4P
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Question
- A company makes solar panels. The company’s revenue function, in dollars, is R(n)=10n , where n is the number of panels produced. The cost function is C(n)=100(2)π/30 . R and C are shown on the graph
below.
a) Estimate from the graph
i) the break-even points
ii) the number of panels that should be produced for maximum profit
b) Write the equation for the profit function P.
c) Graph P.
d) Use your graph of P to estimate the number of panels that give maximum profit.
e) How would your answers for break-even points and maximum profit change if
i) the number of dollars of revenue per panel is increased slightly?
ii) the cost function is C(n)=100(2)π/35 changed to ?
f) What does the number that was changed in part e) ii) represent?
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