Market research for a certain ice cream company indicates that if the price per cup of ice cream is $50.00, the demand will be 1200 cups, whereas if the price is increased to $60.00, the demand will be 1100 cups. 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. (A) Find the value(s) of x at the break-even points. (B) 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.

Market research for a certain ice cream company indicates that if the price per cup of ice cream is $50.00, the demand will be 1200 cups, whereas if the price is increased to $60.00, the demand will be 1100 cups. 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. (A) Find the value(s) of x at the break-even points. (B) 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.

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter12: Algebra Of Matrices

Section12.CR: Review Problem Set

Problem 37CR

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Question

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.

(A) Find the value(s) of x at the break-even points.

(B) 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.

Expert Solution