Question

The Hartnett Corporation manufactures baseball bats with Pudge Rodriguez’s autograph stamped on them. Each bat sells for \(35 and has a variable cost of \)22. There are \(97,500 in fixed costs involved in the production process.

b. Find the sales (in units) needed to earn a profit of \)262,500.

Short answer

The number of units to be sold by the company to earn a profit of $262,500 is 12,692.31.

Step-by-step solution

Information given in the question

Selling price per unit: $35

Variable cost per unit: $22

Fixed cost: $97,500

Required profit: $262,500

Sales (in units)

$\begin{array}{rcl}\mathrm{Sales}\left(\mathrm{in}\mathrm{units}\right)& =& \frac{\left(\mathrm{Profit}+\mathrm{Fixed}\mathrm{cost}\right)}{\left(\mathrm{Revenue}\mathrm{per}\mathrm{unit}-\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}\right)}\\ & =& \frac{\left(\$262,500+\$97,500\right)}{\left(\$35-\$22\right)}\\ & =& 27,692.31\end{array}$