Linear Programming project due Tuesday! Need help!!

[streetglow50]

I have a math project that is due this Tuesday, and everyone i've talked with has had problems understanding my project as well.
Here is the problem (it's big):
A vet has asked you to formulate a diet for a racehorse from two commercially packaged foods. Each pound of food A contains 2 grams of fat, 8 grams of protein, and 16 grams of carbohydrates. Each pound of food B contains 8 grams of fat, 4 grams of protein, and 32 grams of carbohydrates.

The vet has prescribed that the horse receives no more than 384 grams of fat per day from the diet. The horse also needs at least 176 grams of protein and 1024 grams of carbohydrates. The horse should eat no more than 60 pounds of food total. Food A costs $1.20 per pound and food B costs $.75 per pound.

You are you present a diet to the vet with a description of all applicable constraints including definitions for any variables used, a system of inequalities describing the constraints, and a graphic representation of the possible food mixture region. In addition, your report should include the points where the maximum or the minimum costs could occur, the equation you would use to determine the minimum or maximum cost, the number of pounds of each type of food mixed to minimize costs, and the minimum cost.

By using the correct blend of foods, how much did you save the vet versus the maximum costs? if you received 5% of the savings as a bonus, how much did you receive?

 

[jolly]

If everyone is having problems "understanding" your project, why not go directly to the source, aka your teacher, to clear up any confusion?

 

[streetglow50]

My Constraints

Here's the constraints i wrote down:

2A + 8B < 384 grams of fat
8A + 4B > 176 grams of protein
16A + 32B > 1024 grams of carbohydrates
A + B < 60 pounds

I then reduced those down to:

A + 4B < 192 grams fat
2A + B > 44 grams protein
A + 2B > 64 grams carbohydrates
A + B < 60

I'm very confused on what equation to write to find the max and the min. I've tried the guess-and-check method and got some kind of answer, but i need an equation for my presentation on Tuesday...

I got 30 pounds of both for max and then 2lbs of A and 40lbs of B for the min...but again, i just guessed and checked that one

________________
Edited for tone and cohesion - stapel

 

[skeeter]

graph the four lines on the xy plane, using x for A and y for B ...

B = 60 - A
B = (192 - A)/4
B = 44 - 2A
B = (64 - A)/2

you will get a 5-sided region in quadrant I where all points (A,B) on the sides and interior satisfy the requirements from the original inequalities.

from what I remember from linear programming, points of maximization or minimization will occur at the vertices of that pentagonal region.

since minimization of cost is your ultimate goal, substitute the values of each ordered pair (A, B) at each vertex into your cost equation and see which one is the cheapest.

 

[streetglow50]

Wait, how do i solve this inequality?

2A + B > 44
so B= 44 - 2A

Substitution:
2A + 44 - 2A = 44
(subtract 44 on both sides)

2A - 2A = 0
(subtract 2A from 2A)

0 = 0
???? :?

 

[stapel]

Wait, how do i solve this inequality?

2A + B > 44
so B= 44 - 2A

No. If 2B + B > 44, then B > 44 - 2A, not "equal" to 44 - 2A.

Substitution:

Where is this coming from? You're solving a system of inequalities, not a linear system of equations...?

Try using the methods they used in class and in the book: Graph the lines, shade the appropriate sides (to show the inequalities), find the intersection points (corner points) of the enclosed area, and plug them one-by-one into the optimization equation.

Eliz.