A company makes wooden tables and finds that the break even

A company makes wooden tables and finds that the break even quantity is 26. The company also determines that the price p (in dollars) that they charge for each table is $2 more than the marginal cost. Find the fixed cost, assuming that the revenue and cost functions are linear.

Solution

Answer: $52 (As explained below)

Profit on making 26 items = 0____________________________(1)

Also, profit on making 26 items = selling price of 26 items - total cost of 26 items = [ 26 x (marginal cost + 2) ] - [ 26 x marginal cost - fixed cost ] = 26 x marginal cost + 52 - 26 x marginal cost - fixed cost______________(2)

If, M is marginal cost and F the fixed cost, from (1) and (2), we have:

26M + 52 - 26M - F = 0

F = 52