Chapter 7.3, Problem 47E

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Profit A sporting goods manufacturer produces regulation soccer balls at two plants. The costs of producing x 1 units at Location 1 and x 2 units at Location 2 are given by C 1 ( x 1 ) = 0.02 x 1 2 + 4 x 1 + 500 And C 2 ( x 2 ) = 0.05 x 1 2 + 4 x 1 + 275 respectively. If the product sells for $50 per unit, then the profit function for the product is given by P ( x 1 , x 2 ) = 50 ( x 1 + x 2 ) − C 1 ( x 1 ) − C 2 ( x 2 ) Evaluate each of the following.(a) P ( 250 , 150 ) (b) P ( 300 , 200 ) (c) P ( 600 , 400 ) (a) To determine To calculate: The profit of sport goods manufacturer that produces regular soccer balls at two location plats the cost of producing 250 units at Location 1 and 150 units at Location 2. Explanation Given information: A sport goods manufacturer produces regular soccer balls at two location plats the cost of producing x1 units at Location 1 and x2 units at Location 2 given by C1(x1)=0.02x12+4x1+500 and C2(x2)=0.05x22+4x2+275 The product sells for$500 per units, the profit function for the product is given by

P(x1,x2)=50(x1+x2)C1(x1) C2(x2)

Calculation:

Consider the cost of producing x1 units at Location 1 and x2 units at Location 2 given by

C1(x1)=0.02x12+4x1+500 and C2(x2)=0.05x22+4x2+275

And

The product sells for \$500 per units, the profit function for the product is given by

P(x1,x2)=50(x1+x2)C1(x1) C2(x2)

Substitute, C1(x1)=0.02x12+4x1+500 for C1(x1), C2(x2)=0

(b)

To determine

To calculate: The profit of sport goods manufacturer that produces regular soccer balls at two location plats the cost of producing 300 units at Location 1 and 200 units at Location 2.

(c)

To determine

To calculate: The profit of sport goods manufacturer that produces regular soccer balls at two location plats the cost of producing 600 units at Location 1 and 400 units at Location 2.

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