Market research for a certain ice cream company indicates that if the price per cup of ice cream is P50.00, the demand will be 1200 cups, whereas if the price is increased to P60.00, the demand will be 1100 cups. (a) If p denotes the price per cup (in pesos) and x denotes the demand for ice cream (in cups), express p as a linear function of x. (b) Determine the revenue function and its domain. (c) Find the marginal revenue at a production level of 200 cups of ice cream. Interpret.

Algebra and Trigonometry (MindTap Course List)
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ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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1. Market research for a certain ice cream company indicates that if the price per cup of ice
cream is P50.00, the demand will be 1200 cups, whereas if the price is increased to P60.00,
the demand will be 1100 cups.
(a) If p denotes the price per cup (in pesos) and x denotes the demand for ice cream (in
cups), express p as a linear function of x.
(b) Determine the revenue function and its domain.
(c) Find the marginal revenue at a production level of 200 cups of ice cream. Interpret.
Now, suppose it is known that the total cost of production of x cups of ice cream is given by
C(x) = 3x + 25,500.
(d) Find the value(s) of x at the break-even points.
(e) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice
cream. Compare this value with the exact profit from the sale of the 500th cup.
Transcribed Image Text:1. Market research for a certain ice cream company indicates that if the price per cup of ice cream is P50.00, the demand will be 1200 cups, whereas if the price is increased to P60.00, the demand will be 1100 cups. (a) If p denotes the price per cup (in pesos) and x denotes the demand for ice cream (in cups), express p as a linear function of x. (b) Determine the revenue function and its domain. (c) Find the marginal revenue at a production level of 200 cups of ice cream. Interpret. Now, suppose it is known that the total cost of production of x cups of ice cream is given by C(x) = 3x + 25,500. (d) Find the value(s) of x at the break-even points. (e) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice cream. Compare this value with the exact profit from the sale of the 500th cup.
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