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

Algebra ->  Linear-equations -> 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      Log On


   

Question 60901: 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
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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.
:
Let x = number of st playhouse, Let y = number of del playhouses
:
labor equation:
12x + 20y =< 800
20y =< 800 - 12x
y =< (800/20) - (12/20)x
y =< 40 - .6x: plotted as the purple line
:
Quantity equation:
x + y =< 50
y =< 50 - x; plotted as the green line
:
:
Existing orders require the company to produce at least 10 standard playhouses and 15 deluxe playhouses per week.
:
Standard minimum:
x => 10; **
:
Deluxe minimum
y => 15; plotted as the black horizontal line
:
The graph:
+graph%28+300%2C+200%2C+-10%2C+50%2C+-10%2C+50%2C+40-.6x%2C+50-x%2C+15%29+
:
**draw the graph of x => 10 as a vertical line going thru x = 10 (I can't seem to do that on this graph creator.
;
The area of feasibility bounded by:
1. Equal and above the black horizontal line (y=15)
2. Equal and to the right of the vertical line (x=10)
3. Equal and below the purple and green lines, whichever is lower.
:
Make sense to you? any questions?