Chapter 10.3, Problem 35E

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# A firm has monthly average costs, in dollars, given by C ¯ = 45 , 000 x + 100 + x where x is the number of units produced per month. The firm can sell its product in a competitive market for $1600 per unit. If production is limited to 600 units per month, find the number of units that gives maximum profit, and find the maximum profit. To determine To calculate: The number of units which provides maximum profit, and also, calculate the maximum profit. If the average monthly cost (in dollar) is given as, C¯=45000x+100+x Where x is the number of units per month. Explanation Given Information: The provided average monthly cost (in dollar) is given as, C¯=45000x+100+x Where x is the number of units per month. The selling price for the product in competitive market is$1600 per unit. And maximum limit of production is 600 units per month.

Formula Used:

The total profit function is:

P(x)=R(x)C(x)

Where R(x)andC(x) are total revenue function and total cost function.

Calculation:

Consider the average monthly cost (in dollars),

C¯=45000x+100+x

Where x is the number of units per month.

Since, the selling price for the product in competitive market is \$1600 per unit. And maximum limit of production is 600 units per month.

Thus the total profit function is:

P(x)=R(x)C(x)

Let x be the number of persons.

Total cost function can be written as:

C(x)=45000+100x+x2

Total revenue function can be written as:

R(x)=1600x

Now, substitute the values of R(x)andC(x) in the profit formula as, P(x)=R(x)C(x)

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