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 $21,000? (Note that the units sold must account for total production costs (direct and overhead) plus desired profit:

Direct labor hours:                                             0.6 hr / unit

Direct labor costs:                                           $25 / hr

Direct materials cost:                                      $5.1 / unit

Overhead costs:                                                 85% of direct labor

Packaging and shipping:                                  $2.6 / unit

Selling price:                                                     $38 / unit

Explanation / Answer

let no of units be x

direct labor costs= 25* .6* x= 15x

ddirect materials cost= 5.1*x= 5.1x

overhead cost= 15x*.85= 12.75x

packing and shipping= 2.6x

selling price = 38x

total profit=selling price - total costs = 38x - 15x -5.1x-12.75x -2.6x= 2.55x

2.55x= 21000

x=8235.29 = 8236 units

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