Question 119915
 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. 
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There are 380 hours of labor available in the cutting department each day 

:and 330 hours in the sewing department. 
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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: