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.
x2=48-3t= -3t + 48
To find the constraints on t, set each equation (x1 and x2 in terms of t) >= 0. Then solve for t.
x1 = 2t-24 >= 0
So t is in the range 12<=t<=16
t>=0, but that's redundant.
So the answer is B.
x1 = 2t-24
x2 = -3t+48