Question

A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 574,000 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.

Answer 1

Constraints:

x1 + x2 + x3 = 25 [number of rail road tank cars] ----- (i)

7000x1 + 14000x2 + 28000x3 = 574000 [Carrying capacity]

Dividing the second equation by 7000, we get

x1 + 2x2 + 4x3 = 82 ----- (ii)

subtracting (i) from (ii), we get

x1 + x2 + x3 = 25

x2 + 3x3 = 57

now subtracting the second equation from first we get

x1 - 2x3 = -32

x2 + 3x3 = 57

Let us assume the value of x3 as t, so we get

x1 = -32 + 2t

x2 = 57 - 3t

Now, since all of them must be positive, which gives the constraints that t must be greater than 16 and t must be less than 19.

Hence the possible values of t are 16,17,18 and 19

Possible answers are x1=0,x2=9,x3=16

Possible answers are x1=2, x2 =6, x3 = 17

Possible answers are x1=4, x2=3, x3=18

Possible answers are x1=6,x2=0,x3 =19

Note - Post any doubts/queries in comments section.