Math assistance required (linear programming) (1 Viewer)

[Jerry Klawiter]

My wife is running into issues with a particular equation. We are talking 6 hours later and no headway.
The goal is determining the objective and the constraints and solving the equation.
Can somebody add some input, would be much appreciated.

After the hurricanes in Florida in the summer of 2004, FEMA sent disaster relief trucks to the state. Each truck could carry no more than 6000 pounds of cargo. Each case of bottled water weighs 25 pounds and each generator weighs 150 pounds. Due to the number of trucks and the supply of water and generators nationwide, each truck must carry at least 10 generators and the number of cases of water in each truck must be at least 6 times the number of generators. If each generator helps two households and each case of water helps one household, determine the
maximum number of Florida households aided by each truck and how many generators and cases of water should be sent in each truck.

 

[Haggai]

Seems to me you can set it up this way:

G = number of generators in each truck
W = number of cases of water in each truck

10

 

[Jerry Klawiter]

Thank you so much for the help. My head has been spinning all weekend with this trying different scenarios. I'll run the numbers and report back.
Jerry's wife
Suzanne

 

[RichP]

Unless I'm missing something, there's no maximum. That is, there is no max given for number of trucks that can be sent or amount of water/generators.

Was there a number left out? Total number of trucks perhaps?

Without that, you can simply set an arbitrary number of trucks to start with, say 10.

Working from what's given, you know that each truck starts off with a load of 3000lbs. That is 10G @ 150lbs and 60W @ 25lbs.

For each additional generator you add, you must add 6 cases of water for a total additional weight of 1050lbs. So each generator you add increases the truck's load by 1050lbs.

So to max a truck out evenly, you would put 20 generators on, which weigh 3000lbs, and 120 cases of water, which also weighs 3000lbs. That truck would aid 160 households.

Alternatively, if you simply max out the water instead, you get a truck that has 10 generators for 1500lbs and 180 cases of water for 4500lbs. That truck would aid 200 households, and is a better choice if the goal is simply the max number of households aided.

The generators are inefficient, aiding only 2 households per, while the water aids 1 per case, which means for every 150lbs, a generator aids 2 households, while water aids 6. This could be expressed as 150lbs = 1G = 6W.

So it seems logical to max out the amount of water each truck can carry.

 

[Haggai]

Although the wording could maybe have been slightly clearer, it seems that everything is on a per-truck basis. The question is to find "the maximum number of Florida households aided by each truck and how many generators and cases of water should be sent in each truck," so the assumption would be that each truck has exactly the same capacity. The total number of trucks being sent to Florida wouldn't affect things.

 

[Jerry Klawiter]

Thanks guys for adding further comments.
My wife is still somewhat at a loss on this problem.
She will contribute further once she returns home from work this evening.
I am of no help; I am 23+ years removed from post HS education.
I think it would take me longer refreshing the mind then asking for assistance.
Even our daughter that just completed her second year of college math spent several hours without a conclusion.
Math is not my wife’s nor my strongest assets.

 

[Chu Gai]

If that's all the info given, then looks to me like RichP is correct.

 

[Haggai]

Yup. That's what I think it comes out to as well.

 

[Brett_B]

.

 

[Bryan X]

Nevermind. I should have read the whole post to realize the answer was already given before I spent the time to post the answer.