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Question 119921: Transportation An electronics company produces three models of stereo speakers, models A, B, and C, and can deliver them by truck, van, or station wagon. A truck holds 2 boxes of model A, 2 of model B, and 3 of model C. A van holds 3 boxes of model A, 4 boxes of model B, and 2 boxes of model C. A station wagon holds 3 boxes of model A, 5 boxes of model B, and 1 box of model C.
a. If 25 boxes of model A, 33 boxes of model B, and 22 boxes of model C are to be delivered, how many vehicles of each type should be used so that all operate at fullcapacity?
b. Model C has been discontinued. If 25 boxes of model A and 33 boxes of model B are to be delivered, how many vehicles of each type should be used so that all operate at
full capacity?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! An electronics company produces three models of stereo speakers, models A, B, and C, and can deliver them by truck, van, or station wagon.
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A truck holds 2 boxes of model A, 2 of model B, and 3 of model C.
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A van holds 3 boxes of model A, 4 boxes of model B, and 2 boxes of model C.
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A stn wagon holds 3 boxes of model A, 5 boxes of model B, and 1 box of model C.
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a. If 25 boxes of model A, 33 boxes of model B, and 22 boxes of model C are to be delivered, how many vehicles of each type should be used so that all operate at full capacity?
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Let
t = no. of trucks
v = no. of vans
s = no. of stn wagons
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Write 3 equations from the information given
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The model A equation: 2t + 3v + 3s = 25
The model B equation: 2t + 4v + 5s = 33
The model C equation: 3t + 2v + 1s = 22
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Three equations, three unknowns Using the matrix feature on the a Ti83, I got
5 trucks, 2 vans, and 3 stn wagons, which checks out
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b. Model C has been discontinued. If 25 boxes of model A and 33 boxes of model B are to be delivered, how many vehicles of each type should be used so that all operate at full capacity?
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The lack of model C provides more space for the other two models, however,
how much space, is not readily apparent from the information given:
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Perhaps an estimate can be given as follows
Take the spaces gained from the absence of Model C, divide between A & B;
Assign it as follows:
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Truck: 3 model A's and 4 model B's
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Van: 4 model A's and 5 model B's
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Stn Wag: 4 model A's and 5 model B's
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The model A equation: 3t + 4v + 4s = 25
The model B equation: 4t + 5v + 5s = 33
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Using elimination on these two equation, came up with 7 trucks
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Thats 21 Model A's in the 7 trucks , the remaining 4 can go in 1 van
Then: 28 Model B's in the same 7 trucks, then remaining 5 can go in the same van
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I'm going to say 7 trucks and 1 van. Park the station wagon
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Anyway, hope all this is of some use to you. Ankor
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