BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.10, Problem 76E

a.

To determine

Assuming that the relationship between cost and number of chairs produced is linear, find an equation that expresses this relationship. Then graph the equation.

Expert Solution

Answer to Problem 76E

  C=13n+900

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.10, Problem 76E , additional homework tip  1

Explanation of Solution

Calculation:

Assume that the relationship between cost and number of chairs produced is linear, and then the equation that represents this relationship is given as,

  C=mn+b

To manufacture 100 chairs, it costs $2200 . So, substitute n=100 and C=2200 in the equation C=mn+b , we get,

  2200=m(100)+b2200=100m+b............(1)

To manufacture 300 chairs, it costs $4800 . So, substitute n=300 and C=4800 in the equation C=mn+b , we get,

  4800=m(300)+b4800=300m+b............(2)

Subtract equation (2) from equation (1) ,

  4800=300m+b2200=100mb2600=200m13=mm=13

So, the value of m is m=13 .

Now, we substitute the value m=13 in equation (1) , we get:

  2200=100(13)+b2200=1300+bb=900

Put these values of m=13 and b=900 in C=mn+b to get,

  C=13n+900

So, the linear equation that expresses this relationship between cost and number of chairs produced is C=13n+900 .

The graph of the equation C=13n+900 is given below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.10, Problem 76E , additional homework tip  2

Hence, the linear equation that expresses this relationship between cost and number of chairs produced is C=13n+900 and the graph is shown above.

b.

To determine

What is the slope of the line in part (a) and what does it represent?

Expert Solution

Answer to Problem 76E

  13

It represents the cost per number of chairs.

Explanation of Solution

Calculation:

Since, the equation of the line that has slope m and yinterceptb is y=mx+b .

Hence, the slope of the line C=13n+900 is 13 and it represents the cost per number of chairs.

c.

To determine

What is yintercept of this line, what does it represent?

Expert Solution

Answer to Problem 76E

  900

It represents the monthly fixed cost.

Explanation of Solution

Calculation:

Since, the equation of the line that has slope m and yinterceptb is y=mx+b .

Hence, the yintercept of the line C=13n+900 is 900 and it represents the monthly fixed cost.

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