Given the following information, how many units must be sold to achieve a profit

Question

Given the following information, how many units must be sold to achieve a profit of $23,000? (Note that the units sold must account for total production costs (direct and overhead) plus desired profit.)

                                Direct labor hours:                                             0.4 hr / unit

                                Direct labor costs:                                           $23 / hr

                                Direct materials cost:                                      $4.5 / unit

                                Overhead costs:                                                 100% of direct labor

                                Packaging and shipping:                                  $2.1 / unit

                                Selling price:                                                     $29 / unit

Explanation / Answer

Let the number of units added be 'A'

Profit = AxSelling price - (Ax Direct labor hoursx  Direct labor costs + AxDirect materials cost +  Overhead costs + Ax Packaging and shipping)

Profit = Ax29 - Ax(0.4x23 + 4.5 + (100/100)x 0.4x23 + 2.1) = 29A - 25A = 4A

Since, Profit = 23,000
A = 23,000/4 = 5750 units

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