\ \

Consider $\"\"$ is the number of racing skates manufactured and $\"\"$ is the number of figure skates manufactured. \ \

The profit function is $\"\"$ . \ \

Hence $\"\"$ is the objective function to be maximized. \ \

The constraints are : \ \

The positive number of skates must be manufactured then $\"\"$ , $\"\"$ . \ \

Only $\"\"$ hours are available for fabrication then $\"\"$ . \ \

Only $\"\"$ hours are available for finishing then $\"\"$ . \ \

Graph : \ \

Graph the constraints. \ \

$\"\"$ \ \

\ \

Observe the graph the corner points are $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

The function is $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

The maximum profit is $\"\"$ when $\"\"$ racing skates and $\"\"$ figure skates are produced. \ \

The maximum profit is $\"\"$ when $\"\"$ racing skates and $\"\"$ figure skates are produced.