Question 119921
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