## Precalculus (6th Edition) Blitzer

50 regular and 100 deluxe jet skis, and the profit is $\$35,000$. #### Work Step by Step Let us assume that x is the number of regular jet skis and y is the number of deluxe jet skis. Then, from the given information, the objective function is given below:$ z=200x+250y $And to maximize the profit, the constraints on the basis of the given information are as given below:$\begin{align} & x\ge 50 \\ & y\ge 75 \\ \end{align}$And$ x+y\le 150$Use a graphical method to find the values of x and y. Now, plot the graph for the inequalities with the feasible region. Let us consider the corner points from the graph plotted$ A\left( 50,75 \right),B\left( 75,75 \right)$and$ C\left( 50.100 \right)$. Put the value of the x and y coordinates in the objective function for each corner point to compute the maximum profit as given below: At corner point$ A\left( 50,75 \right)$,$\begin{align} & z=200\left( 50 \right)+250\left( 75 \right) \\ & =28,750 \end{align}$At corner point$ B\left( 75,75 \right)$,$\begin{align} & z=200\left( 75 \right)+250\left( 75 \right) \\ & =33,750 \end{align}$At corner point$ C\left( 50,100 \right)$,$\begin{align} & z=200\left( 50 \right)+250\left( 100 \right) \\ & =35,000 \end{align}$The profit function is maximum at the corner point$ C\left( 50,100 \right)$. Thus, the company needs to manufacture$50$regular and$100$deluxe jet skis to maximize the profit, and with the maximum profit of$\$35,000$. 