Question

A company produces doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets.

Answer 1

x = number of doll houses; y = furniture sets
:
The labor constraint:
3x + 8y =< 400
Arrange in the general (y=) form so we can plot the graph
8y =< 400 - 3x
y =< (400/8) - (3/8)x
y =< 50 - (3/8)x
:
The production constraint:
x + y =< 100
y =< 100 - x
:
Min house constraint:
x => 20
:
Min furniture constraint
y => 10
:
Plot the Labor equation; I assume you know how to substitute for x and find y


x | y
-------
0 | 50
8 | 47
32 | 38
:
Plot the production restraint
x | y
------
0 |100
20 | 80
50 | 50
:
x => 20 is at or to the right of a vertical line going thru x=20
:
y => 10 is at or above a horizontal line going thru y = 10
:
Look something like this:

:
Area of feasibility:
1. At or below the green or purple lines which ever is lowest
2. At or above the horizontal line at y = 10
3. At or to the right of vertical line at x=20

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