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Question 758759: A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The trick ski requires 6 labor hours for fabricating and 1 labor hour for finishing. The slalom ski requires 4 labor hours for fabricating and 1 labor hour for finishing. The maximum labor hours available per day for fabricating and finishing are 108 and 24, respectively. If X is the number of trick skis and Y is the number of slalom skis produced per day, write a system of linear inequalities that indicates appropriate restraints on X and Y. Find the set of feasible solutions graphically for the number of each type of ski that can be produced.
Please help me with this, I am totally lost. Please expalin the steps so I'll understand how to solve these problems.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! company makes two types of water skis, a trick ski and a slalom ski.
The trick ski requires 6 labor hours for fabricating and 1 labor
hour for finishing.
The slalom ski requires 4 labor hours for fabricating and 1 labor
hour for finishing.
The maximum labor hours available per day for fabricating and
finishing are 108 and 24, respectively.
If X is the number of trick skis and Y is the number of slalom skis
produced per day, write a system of linear inequalities that
indicates appropriate restraints on X and Y.
Find the set of feasible solutions graphically for the number of each type of ski that can be produced.
:
Fabricating equation
6x + 4y <= 108
:
Finishing equation
1x + 1y <= 24
:
since you can make negatives skis
x => 0
y => 0
:
Find the set of feasible solutions graphically for the number of each
type of ski that can be produced.
We have to put the equations into the slope/intercept to graph
6x + 4y = 108
4y = -6x + 108
divide by 4
y = -1.5x + 27; Red
and
x + y = 24
y = -x + 24; Green
Graph these two equations
The feasibility region is at or below the area bounded by the points
x=0, y=24; x=6, y=18; x=18; y=0
:
you can prove this to yourself using the fabricating equation
6x + 4y <= 108
x=6 trick skies, y=18 salom skies
6(6) + 4(18) =
36 + 72 = 108 total hrs
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