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 \\ (P(x)+300)/(30)=x \\ (P(x))/(30)+(300)/(30)=x \\ (1)/(30)P(x)+10=x \end{gathered}`

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

`y=(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=(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