Answer
the maximum value of weekly profit is\[\$35,000\], and the number of jet skis will be 50.
Work Step by Step
Step I:
From the given constraints, draw all the lines and their region.
In the first constraints:
\[x\ge 0\], it is the region where x takes only positive values.
In the second constraints:
\[y\ge 0\], it is the region where y takes only positive values.
In the third constraints:
\[x+y\le 150\].
Draw first, \[x+y=150\].
It is the line with
\[\begin{align}
& x-\text{intercept}=150 \\
& y-\text{intercept}=150 \\
\end{align}\]
Now, put \[x=0,\text{ and }y=0\].
Which gives, \[0\le 150\], which is true, it means region contains the origin.
In the fourth constraints:
\[x\le 50\], it is the region where xcantake only50 or less than 50.
In the fifthconstraints:
\[y\le 75\], it is the region where ycan take only 75 or less than 75.
Step II:
The corner values are:
\[A\left( 50,75 \right),\text{ }B\left( 50,100 \right),\text{ and }C\left( 75,75 \right)\]
Step III:
The value of the objective function at a point\[A\left( 50,75 \right)\]is:
\[\begin{align}
& z=200\times 50+250\times 75 \\
& =28,750
\end{align}\]
The value of the objective function at a point\[B\left( 50,100 \right)\]is:
\[\begin{align}
& z=200\times 50+250\times 100 \\
& =35,000
\end{align}\]
The value of the objective function at a point\[C\left( 75,75 \right)\]is:
\[\begin{align}
& z=200\times 75+250\times 75 \\
& =33,750
\end{align}\]
Therefore, the maximum value of weekly profit is\[\$35,000\], and the number of jet skis will be 50.
