Question

The revenue for selling a units of a product is R = 40z. The cost of producing a units is C = 20z + 7000. In order to obtain a profit, the revenue must be greater than thecost, so we want to know, for what values of x will this produce return a profit.To obtain a profit, the number of units must be greater than ____

Answer 1

Given

• The revenue for selling ,z, units of a product: R = 40z.

,

• The cost of producing ,z, units is C = 20z + 7000.

Explanation

To obtain a profit, the revenue must be greater than the cost of producing the units. Then, we can write and solve the following inequality.

$\begin{gathered} R>C \\ 40z>20z+7000 \\ \text{ Subtract 20z from both sides} \\ 40z-20z\gt20z+7000-20z \\ 200z\gt7000 \\ \text{ Divide by 200 from both sides} \\ \frac{200z}{200}\gt\frac{7000}{20} \\ z>350 \end{gathered}$Answer

To obtain a profit, the number of units must be greater than 350.