SOLUTION: A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited

A home-based company produces both hand-knitted scarves and sweaters.
The scarves take 2 hours of labor to produce, and the sweaters take 14 hours.
The labor available is limited to 40 hours per week, and the total production
capacity is 5 items per week.  Write a system of inequalities representing
this situation, where x is the number of scarves and y is the number of
sweaters.  Then graph the system of inequalities. THANK YOU IN ADVANCE

Each scarf takes 2 hours of labor. Therefore x scarves takes 2x hours of
labor. Each sweater takes 14 hours of labor. Therefore x sweaters takes 14y
hours of labor

Therefore the total number of hours of labor is 2x + 14y.

Since the number of hours of labor must be less than or equal to 40, we 
have the inequality:

         2x + 14y < 40

Since they are limited to x items per week,

            x + y < 5

Now there are two additional inequalities, the obvious ones, which
indicate that the number of each item cannot be negative.  These are

                x > 0
                y > 0

These last two limit the graph to the upper right hand region of
the xy-plane.  So we draw the graphs of the lines we get by 
replacing the inequalities by equal signs.

2x + 14y = 40
   x + y = 5
       x = 0  (the y axis)
       y = 0  (the x axis)




Shade the region which is below both the red and the green 
lines, which is above the x-axis and to the right of the 
y-axis. This is the feasible region.

Edwin McCravy