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.

x1+x2+t=24

x1=24-x2-t

7000x1+14000x2+28000t=504000

7000(24-x2-t)+14000x2+28000t=504000

168000-7000x2-7000t+14000x2+28000t=504000

7000x2+21000t=336000

7000x2=336000-21000t

x2=48-3t= -3t + 48

x1+48-3t+t=24

x1-2t=-24

x1=2t-24

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

2t>=24

t>=12

x2=-3t+48>=0

-3t>=48

t<=16

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

x3=t

12<=t<=16