Question

The Tonka Toy Company has a profit of P(x)=30x-300 dollars when d RC Trucks are sold a month. 1. Find an inverse function for this model. Show work. 2. Use the inverse to find the amount of Trucks needed to produce a profit of $20,000. Show work.

Answer 1

1. The inverse function is found isolating x, as follows:

$\begin{gathered} P(x)=30x-300 \\ P(x)+300=30x \\ \frac{P(x)+300}{30}=x \\ \frac{P(x)}{30}+\frac{300}{30}=x \\ \frac{1}{30}P(x)+10=x \end{gathered}$

Changing the name of the variables, the inverse function is:

$y=\frac{1}{30}x+10$

where y represents the amount of trucks and x the profit.

2. Replacing with x = 20,000 into the inverse function, we get:

$\begin{gathered} y=\frac{1}{30}\cdot20000+10 \\ y=666.67+10 \\ y=676.67 \end{gathered}$

The amount of Trucks needed to produce a profit of $20,000 is 677