MATH SOLVE

3 months ago

Q:
# The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $65,000. The variable cost of recapping a tire is $7.5. The company charges$25 to recap a tire. a. For an annual volume of 15, 000 tire, determine the total cost, total revenue, and profit. b. Determine the annual break-even volume for the Retread Tire Company operation.

Accepted Solution

A:

Part a) Total CostTotal Cost for recapping the tires is the sum of fixed cost and the variable cost. i.e.The total cost is ( $65,000 fixed) + (15,000 x $7.5)=$65,000+$112,500=$177,500 Part b) Total RevenueRevenue from 1 tire = $25Total tires recapped = 15000So, Total revenue = 15000 tires x $25/tireTotal Revenue =$375,000 Part c) Total ProfitTotal Profit = Revenue - CostUsing the above values, we get:Profit = $375,000 - $177,500Profit = $197,500 Part d) Break-even PointBreak-even point point occurs where the cost and the revenue of the company are equal. Let the break-even point occurs at x-tires. We can write:For break-even pointCost of recapping x tires = Revenue from x tires65,000 + 7.5 x = 25x 65,000 = 17.5 xx = 3714 tiresThus, on recapping 3714 tires, the cost will be equal to the revenue generating 0 profit. This is the break-even point.