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

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Question 122693: A small company produces both standard and deluxe playhouses. The standard playhouses take 12 hours of labor to produce and the deluxe playhouses takes 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. 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.
:
Let x = standard p.h; y = deluxe p.h
:
The labor equation:
12x + 20y =< 800
:
put equation in the general (y=) form to plot the graph
20y =< 800 - 12x
y =< 800/20 - (12/20)x
y =< 40 - .6x
:
:
The production capacity equation:
x + y =< 50
Put this in the "y=" form also
y <= 50 -x
:
Existing order constraints
x => 10
and
y => 15
:
Plot these using the equation givens.
y = 40 - .6x; (purple line)
y = 50 - x; (green line)
y = 15; Note that y = 15 is a horizontal line going thru y = 15; black line
x = 10 is a vertical line going thru x = 10
:
I assume you know how to make up an x/y table and plot a graph, for each of these equations
:
Here is the graph:

:
That feasibility area is:
1.At or below, the purple line or the green line whichever is lower.
2.At or above the black horizontal line
3.At or to the right of the vertical line