Question

Bradley Co. sells a product with variable costs of $50 per unit and a sales price of $75 each. Bradley has fixed costs of $100,000 and desires a profit of $25,000. If the Company is able to reduce its variable cost per unit to $35 while holding all other items constant, the number of units that must be sold to earn the desired profit will?

Answer 1

Bradley Co. must sell 1250 units to achieve a $25,000 profit after reducing the variable cost per unit to $35, assuming a fixed cost of $100,000 and a sales price of $75 per unit.

Step-by-step explanation:

Profit Maximization Calculation

The student is asking about the number of units Bradley Co. must sell to earn a desired profit if the variable cost per unit is reduced, keeping all other factors constant. Initially, the company sells its product at $75 with variable costs of $50 and fixed costs of $100,000; desiring a profit of $25,000. When the variable cost is reduced to $35, the contribution margin per unit increases, which in turn reduces the number of units that need to be sold to achieve the desired profit.

To find the number of units needed to reach the desired profit after the change in variable cost, we use the formula:

Units Required = (Fixed Costs + Desired Profit) / (Sales Price - New Variable Cost).

By substituting the given values, Units Required = ($100,000 + $25,000) / ($75 - $35) = 1250 units. Therefore, Bradley Co. must sell 1250 units to earn the desired profit of $25,000 with the reduced variable cost of $35.