A chemical manufacturer wants to lease a fleet of 28 railroad tank cars with a combined carrying capacity of 406,000 gallons. Tank cars with three different carrying capacities are available: 7,000 gallons, 14,000 gallons, and 28,000 gallons. How many of each type of tank car should be leased?

Let x1 be the number of cars with a 7,000 gallon capacity, x2 be the number of cars with a 14,000 gallon capacity, and x3 be the number of cars with a 28,000 gallon capacity. Select the correct choice below and fill in the answer boxes within your choice.

multiple choice

A.

The unique solution is

x1=____,

x2=_____,

and

x3=______.

(Simplify your answers.)

B.

There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations

x1=_____t+(_____),

x2=_____t+(_____),

and

x3=t

for

______t_____.

(Simplify your answers. Type integers or simplified fractions.)

C.

There is no solution.