   Chapter 9.9, Problem 37E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

If the daily cost per unit of producing a product by the Ace Company is 10   +   0.1 x dollars and the price on the competitive market is $70, what is the maximum daily profit the Ace Company can expect on this product? To determine To calculate: The maximum profit that the Ace Company earns daily on the product produced by the Ace Company. Explanation Given Information: The cost of producing a product daily is 10+0.1x dollars. The price that the Ace Company charges for one unit of the product is$70.

Formula used:

The power rule of differentiation:

ddxxn=nxn1

Calculation:

Consider the provided cost for 1 unit of the product, 10+0.1x. Thus, for x units of the product, the cost function is

C(x)=x(10+0.1x)=10x+0.1x2

The revenue earned from one unit of the product is \$70. Thus, for x units of the product, the revenue function is represented as,

R(x)=70x

The profit function is calculated by subtracting the revenue and cost functions,

P(x)=R(x)C(x)=70x10x0.1x2=60x0.1x2

To find the maximum profit, differentiate the profit function with respect to x,

P(x)=ddx(60x0.1x2)=ddx(60x)ddx(0.1x2)=60ddx(x)0

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