(a)

A factory is making skirts and dresses from the same fabric.

Each skirt requires hour of cutting and hour of sewing.

Each dress requires hours of  cutting and hour of sewing.

There are hours available each week for  the cutting and hours for sewing.

Profit for each skirts is $ .

Profit for each dress is $ .

Let be the number of skirts designed per week.

Let be the number of dresses designed per week.

The objective function is , where and .

The constraints are

.

(b)

Graph :

Graph the inequalities and shade the required region.

Note : The shaded region is the set of solution points for the objective function.

Observe the graph,

Tabulate the solutions of each of two system of inequalities and obtain the intersection points. 

\ System of boundary equations \	\ \   \	\ \ \	\ \ \	\ \ \
Solution (vertex points)

(c)

Find the value of objective function at the solution points.

At point , .

At point , .

At point , .

At point , .

The factor makes skirts and dresses for a maximum profit of .

The factor makes skirts and dresses for a maximum profit of .