Answer:
[tex]\arge\boxed{\large\boxed{\$ 117,788}}[/tex]
Explanation:
Assume the cost equation to be:
[tex]Cost(x)=Fixed\text{ }costs+Variable\text{ }costs\\\\Cost(x)=A+Bx[/tex]
Where [tex]x[/tex] 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:
[tex]Average\text{ }cost(x)=Cost(x)/x\\\\Average\text{ }cost(x)=(A+Bx)/x\\[/tex]
You are given that the average cost per unit of a production level of 7,700 bats is $14, then:
[tex]14=(A+7,700B)/7,700[/tex]
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:
[tex]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[/tex]
Now you can complete the cost equation:
[tex]Cost(x)=\$ 22,500+11.08x[/tex]
And to predict the total costs for 8,600 bats you must subsitute x with 8,600 in the previous equation:
[tex]Cost(8,600)=\$ 22,500+11.08(8,600)=\$ 117,788[/tex]
