Chapter 10.3, Problem 36E

### 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 small business has weekly average costs, in dollars, of C ¯ = 100 x + 30 + x 10 where x is the number of units produced each week. The competitive market price for this business’s product is $46 per unit. If production is limited to 150 units per week, find the level of production that yields maximum profit, and find the maximum profit. To determine To calculate: The level of production which provides maximum profit, and also, calculate the maximum profit. If the average weekly cost (in dollar) is given as, C¯=100x+30+x10 Where x is the number of units produced per week. Explanation Given Information: The provided average weekly cost (in dollar) is given as, C¯=100x+30+x10 Where x is the number of units produced per week. The selling price for the product in competitive market is$46 per unit. And maximum limit of production is 150 units per week.

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 provided average weekly cost (in dollars),

C¯=45000x+100+x

Where x is the number of units per week.

Since, the selling price for the product in competitive market is \$54 per unit. And maximum limit of production is 150 units per week.

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¯=100x+30+x10

Total revenue function can be written as:

R(x)=46x

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

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