I understand the problems that give various constraints and ask to maximize or minimize something, but not this type.
A chem manufacturer wants to rent a fleet of 24 tank cars with a combined carrying capacity of 504,000 gallons. Tank cars with three capacities are available: 7000 gallons, 14,000 gallons, 28,000 gallons. How many of each should be leased?
Set x, y and z as the three different capacity cars.
There are various answers. For example it can be 18 z's, or 17 z's and 2 y's, or 17z's and 4 x's.
The answer asks to express it as:
x=_t+_ y=_t+_ and z=t where _<=t<=_
that's something times t plus something, etc. where something <=t<=something
Dec 11th 2011, 11:06 PM
Re: Linear Programming
Determined the answer.
7000 gallon car = x1
14000 gallon car = x2
28000 gallon car = x3
Two equations from the given information:
x1+x2+x3=24 The number of the combined tank cars must be 24
7000x1+14000x2+28000x3 = 504000 Their combined capacity must be 504000
There are two equations with three unknowns. That can't be solved unless we select a value for one variable.
Call x3=t. Now solve for the other two variables in terms of t.