Question 801341: A soft-drink distributor has budgeted $300000 for the purchase of 12 new delivery truck. If a model A truck costs $18000, a model B truck costs $22000, and a model C truck costs $30000, how many truck of each model should the distributor purchase to use exactly all the budgeted funds?
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! x, y, z, the counts of truck models A, B, C.
Each of x, y, z must be greater than or equal to zero.
Form these two equations:
 and  .
The cost equation should be divided by 1000 to simplify:
and further divided by 2:
The system is now best shown as
and .
One more equation would be helpful but no other information was given to allow any formation of it. Because the system is more sensitive to z, my idea is try to eliminate this variable.
Multiply the truck count equation by 15 and subtract the simplified cost equation:
The positive integer values for x and y would be:
(1,6), (3,3), maybe (5,0), none others. A graph was made to help identify these.
Going back to either of the original simplified equations of the system, here arbitrarily choosing x+y+z=12, and SOLVE FOR z, we can check the three points just identified and choose any one of them which gives us a z value of positive integer (or zero).
Check (1,6).
Check (3,3).
 .
Check (5,0).
 .
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So the three dimensional points which SHOULD work but should also be checked in the cost equation may be points (x,y,z):
(1,6,5), (3,3,6), and (5,0,7).
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CONFIRMING ANSWERS:
CHECK USING SIMPLIFIED COST ----------
9*1+11*6+15*5=150, TRUE. (1,6,5) is GOOD.
9*3+11*3+15*6=150, TRUE. (3,3,6) is GOOD.
9*5+0+15*7=150, TRUE. (5,0,7) is GOOD.
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