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Question 119915: Production Turley Tailor Inc. makes long-sleeve, shortsleeve,
and sleeveless blouses. A long-sleeve blouse
requires 1.5 hours of cutting and 1.2 hours of sewing. A
short-sleeve blouse requires 1 hour of cutting and .9 hour of
sewing. A sleeveless blouse requires .5 hour of cutting
and .6 hour of sewing. There are 380 hours of labor available
in the cutting department each day and 330 hours in
the sewing department. If the plant is to run at full capacity,
how many of each type of blouse should be made each day?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Inc. makes long-sleeve, short-sleeve,and sleeveless blouses.
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A long-sleeve blouse requires 1.5 hours of cutting and 1.2 hours of sewing.
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A short-sleeve blouse requires 1 hour of cutting and .9 hour of sewing.
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A sleeveless blouse requires .5 hour of cutting and .6 hour of sewing.
:
There are 380 hours of labor available in the cutting department each day
:and 330 hours in the sewing department.
:
If the plant is to run at full capacity,how many of each type of blouse should be made each day?
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Let the 3 types be:
x = no. of long-sl
y = no. of short-sl
z = no of no-sl
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Total cutting hrs is 380, write the cutting equation:
1.5x + 1y + .5z = 380
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Total sewing hrs is 330, write the sewing equation
1.2x + .9y + .6z = 330
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The problem here is we have 3 unknowns and 2 equations;
Choose a value for z that will ensure that x & y will have integer solutions
I chose z = 100 no-sl
:
1.5x + 1y + .5(100) = 380
1.5x + 1y + 50 = 380
1.5x + 1y = 380 - 50
1.5x + 1y = 330
and
1.2x + .9y + .6(100) = 330
1.2x + .9y + 60 = 330
1.2x + .9y = 330 = 60
1.2x + .9y = 270
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Solve these two equations by elimination
Multiply the 1st 2 unknown equation by 12 & the 2nd by 15; we have:
18x + 12y = 3960
18x + 13.5y = 4050
--------------------subtracting eliminates x, find y
0x - 1.5y = -90
y = -90/-1.5
y = 60 short-sl
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Find x using 1.5x + 1y = 330
1.5x + 60 = 330
1.5x = 330 - 60
1.5x = 270
x = 270/1.5
x = 180 long-sl shirts
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We have one solution: x = 180; y = 60; z = 100; will utilize total capacity
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Check solution in the sewing equatioon
1.2(180) + .9(60) + .6(100) =
216 + 54 + 60 = 330 hr
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You can check the solution in the cutting equation:
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