College Math Word Problem

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mickdano

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I could not find an example in my text nor could I find one in previous assignments. Could someone please show me how to do this one?

A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 350,000 gallons. Tank cars with three different carrying capacities are available: 5,000 gallons, 10,000 gallons, and 20,000 gallons. Letting t= number of 20,000 railroad tank cars in the fleet, 2t-20 5,000- gallon railroad tank cars, and -3t+45 10,000 gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing a 5,000-gallon tank car is $550 per month, a 10,000-gallon tank car is $750 per month, and a 20,000-gallon tank car is $1350 per month. Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leasing cost?

How many 5,000-gallon tank cars?
How many 10,000-gallon tank cars?
How many 20,000-gallon tank cars?

The answer is entered as how many of each would total the amount needed. It is in a test, so if anyone could show me... the sooner the better. Thank you so much!
 
\(\displaystyle If \ we \ used \ reduced \ roll \ echelon \form \ we \ get \ x \ = \ 2t-20, \ y \ = \ -3t+45, \ and \ z \ = \ t.\)

\(\displaystyle Hence, \ 10 \ \le \ t \ \le \ 15, \we \ can't \ have \ - \ railroad \ cars.\)

\(\displaystyle Therefore, \ the \ cheapest \ way \ is \ 0(\$550)+15(\$750)+10(\$1350) \ = \ \$24,750.\)
 
BigGlenntheHeavy said:
\(\displaystyle If \ we \ used \ reduced \ roll \ echelon\)
Click to expand...

:idea: Increase the roll, by dumping a few thousand gallons of chemicals along the way.

 


As Glenn shows, the entire exercise requires only solving two inequalities and evaluating a linear expression.

Most of the wording in that exercise is padding.

Glenn solved the following two inequalities, to determine the "domain" of t (by the way, it's not called the "range" of t); that is, the possible values of t, and then he evaluated the linear function below using the lowest value of t in the domain (which turns out to be 10).

2t - 20 ? 0

-3t + 45 ? 0

Monthly Lease Cost = 200t + 22750

This cost formula is a simplification of the linear function: 550(2t - 20) + 750(-3t + 45) + 1350t

 
Re:

mmm4444bot said:
BigGlenntheHeavy said:
\(\displaystyle If \ we \ used \ reduced \ roll \ echelon\)
Click to expand...

:idea: Increase the roll, by dumping a few thousand gallons of chemicals along the way.
Click to expand...

I'm sorry.....

"roll" echelon

Isn't it "row-echelon"??
 
Ok. Amazing! I didn't see anything about the process in my Finite Math text.
Thank you both very much!
 
Mrspi said:
Isn't it "row-echelon"?
Click to expand...

But, Mrs. Pi, these are railroad cars.

As I'm sure the engineer will tell you, the echel'n keeps roll'n along.

I believe that we could use increased roll echelon, if they were to dump some cargo into the watershed.

 
mickdano said:
I could not find an example in my text nor could I find one in previous assignments. Could someone please show me how to do this one?

A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 350,000 gallons. Tank cars with three different carrying capacities are available: 5,000 gallons, 10,000 gallons, and 20,000 gallons. Letting t= number of 20,000 railroad tank cars in the fleet, 2t-20 5,000- gallon railroad tank cars, and -3t+45 10,000 gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing a 5,000-gallon tank car is $550 per month, a 10,000-gallon tank car is $750 per month, and a 20,000-gallon tank car is $1350 per month. Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leasing cost?

How many 5,000-gallon tank cars?
How many 10,000-gallon tank cars?
How many 20,000-gallon tank cars?

The answer is entered as how many of each would total the amount needed. It is in a test, so if anyone could show me... the sooner the better. Thank you so much!
Click to expand...

And he gets full credit without lifting a finger!!!!
 
Actually, I'm a she. Every attempt I make at the question it will give me a new set of numbers to attempt. So although the questions are the same, the numbers change. Test was due, so I had to get it done. I use the same example with different numbers. Thanks for noticing though! ;-)
 
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