Simple Equations

Question

A firm manufuctures a commodity that costs $20 per unit to produce. In addition, the firm has fixed costs of $2000. Each unitis sold for $75. How many units must be sold if the firm is to have a profit of $14500?

Answer 1

The underlying formula that you want to use to solve this one is

Profit = (Selling Price Per Unit - Cost Per Unit) x Number of Units - Fixed Costs, meaning that

Number of Units = (Profit + Fixed Costs) / (Selling Price per Unit - Cost per Unit)

For this set of values that equation becomes

Number of Units = (14500 + 2000) / (75 - 20) = 16500 / 55 = 300

So to achieve a profit of $14,500, the firm must sell 300 units

Answer 2

If the number of units produced and sold is denoted by Q, then the revenue of the firm is 75Q and the total costs of production is 20Q + 2000. Because profit is the difference between total revenue and total cost, it can be written as 75Q - (20Q + 2000).

Because we want the profit to be 14500, the equation

75Q - (20Q + 2000) = 14500

must be satisfied. It is easy to find the solution Q = 16500/55= 300 units.

Q = 300 units