A company produces a product with a variable cost of $7 per unit and fixed costs of $70000. Each unit sells for $15. We need to determine the number of units that must be sold to earn a profit of $30000.

1. Problem Description

A company produces a product with a variable cost of $7 per unit and fixed costs of$

7

0

0

0

0. Each unit sells for $

1

5. We need to determine the number of units that must be sold to earn a profit of $

3

0

0

0

0.

2. Solution Steps

Let $x$ be the number of units sold.

The total revenue is the selling price per unit multiplied by the number of units sold, which is $15x$.

The total cost is the sum of the fixed costs and the variable costs. The variable costs are the variable cost per unit multiplied by the number of units sold, which is $7x$. So the total cost is $70000 + 7x$.

The profit is the total revenue minus the total cost. We want the profit to be $

3

0

0

0

0. Therefore, we have the equation:

$15x - (70000 + 7x) = 30000$

Simplify the equation:

$15x - 70000 - 7x = 30000$

$8x - 70000 = 30000$

$8x = 30000 + 70000$

$8x = 100000$

$x = \frac{100000}{8}$

$x = 12500$

3. Final Answer

The company must sell 12500 units to earn a profit of $30000.