SOLUTION: A small company produces both standard and deluxe playhouses. The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours. The labor availa

A small company produces both standard and deluxe playhouses. The standard
playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20
hours. The labor available is limited to 800 hours per week, and the total
production capacity is 50 items per week. Existing orders require the company
to produce at least 10 standard playhouses and 15 deluxe playhouses per week.
Write a system of inequalities representing this situation, where x is the
number of standard playhouses and y is the number of deluxe playhouses. Then
graph the system of inequalities.

To fill the orders, we must have x > 10 and y > 15

To keep within production capacity, x + y < 50

The x standard ones take 12x hours of labor per week
The y deluxe ones take 20y hours of labor per week

The total hours of labor must not exceed 800 hours, so

          12x + 20y < 800

So we have these inequalities
x > 10  (The area on or to the right of the green line x = 10)
y > 15  (The region on or above the blue line y = 15 
x + y < 50 (The region on or below the grey line x + y = 50
12x + 20y < 800 (The region on or below the purple line 12x + 20y = 800

 

Below is the region called the "feasible region".  It is
the region which satisfies all the inequalities. You can just
shade it on the above graph. 

 

Edwin