Question 240187: A company designs and sells two types of rings: the VIP and the SST. The company can produce up to 24 rings each day using up to 60 total hours of labor. It takes 3 hours to make one VIP ring, and 2 hours to make one SST ring. How many of each type of ring should be made daily in order to maximize profit, if profit on a VIP ring is $30 and profit on an SST ring is $40? What is the profit?
So far I have come up with this not sure if its correct?
x=# of rings to VIP
y=# of rings to SST
3x+2y< or equal to 60
x+y< or equal to 2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A company designs and sells two types of rings: the VIP and the SST.
The company can produce up to 24 rings each day using up to 60 total hours of labor. It takes 3 hours to make one VIP ring, and 2 hours to make one SST ring. How many of each type of ring should be made daily in order to maximize profit, if profit on a VIP ring is $30 and profit on an SST ring is $40? What is the profit?
So far I have come up with this not sure if its correct?
x=# of rings to VIP
y=# of rings to SST
3x+2y< or equal to 60
x+y< or equal to 24
Profit = 30x+40y
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Graphs:
3x+2y <= 60
y <= (-3/2)x + 30
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x+y <= 24
y <= -x+24
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Find the intersection of the two boundary lines:
-x+24 = (-3/2)x+30
(1/2)x = 6
x = 12 so y = 12
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Check (0,0),(0,24),(20,0), (12,12) in the profit equation to determine the max pair.
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Profit = 30x+40y
P(0,0)=0 ; P(0,24)=40*24=960;P(20,0)=30*20=600;P(12,12)=30*12+40*12 = 840
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Max comes from x = 0, y = 24
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Cheers,
Stan H.
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