Question

The Akron Slugger Company produces various types of wooden baseball bats. It has calculated the average cost per unit of a production level of 7 comma 700 bats to be $ 14. If $ 22 comma 500 of the costs are​ fixed, and the plant manager uses the cost equation to predict total​ costs, her forecast for 8 comma 600 bats will be​ (Round any intermediary calculations to the nearest​ cent.)

Answer 1

Answer:

$\arge\boxed{\large\boxed{\ 117,788}}$

Explanation:

Assume the cost equation to be:

                $Cost(x)=Fixed\text{ }costs+Variable\text{ }costs\\\\Cost(x)=A+Bx$

Where $x$ is the number of units (wooden baseball bats) produced.

The average cost per unit of production level is the total cost divided by the number of units produced:

              $Average\text{ }cost(x)=Cost(x)/x\\\\Average\text{ }cost(x)=(A+Bx)/x$

You are given that the average cost per unit of a production level of 7,700 bats is $14, then:

             $14=(A+7,700B)/7,700$

You are also given that the fixed costs are $22,500, thus A = 22,500. Hence, you can substitute the value of A in the previous equation and find B:

              $14=(22,500+7,700B)/7,700\\\\14\times 7,700=22,500+7,700B\\\\107,800-22,500=7,700B\\\\85,300/7,700=B\\\\B=11.08$

Now you can complete the cost equation:

             

               $Cost(x)=\ 22,500+11.08x$

And to predict the total costs for 8,600 bats you must subsitute x with 8,600 in the previous equation:

             $Cost(8,600)=\ 22,500+11.08(8,600)=\ 117,788$