Need Finite Math question solved, please provide work as well. Thank you. 19. A

Question

Need Finite Math question solved, please provide work as well. Thank you.
19. A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 532,000 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? Letx1 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. 0 A. The unique solution is x 1 = , and x3 (Simplify your answers.) There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x 1 = x2 = Simplify your answers. Type integers or simplified fractions.) B. -), and x3°t for sts ° C. There is no solution.

Explanation / Answer

First we try to make a linear equation with the data given to us in the question:

So, 7000x1+14000x2 + 28000x3 = 532000

7x1+14x2+28x3 = 532

(x1)+(2x2)+(4x3) = 76
Now, (x1,x2,x3) can be (76,0,0) or (38,19,0) or (0,0,19)..and more.

Hence, multiple combos of how tank cars should be leased are possible,

x3 = t, 0<=t<=19
x2 =-2t+(76-x1 )/2
x1 = -4t+76-2x2

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