CODEWITHSUNDEEP
matlab
user1810514
user1810514

Reputation: 47

Linear equations MATLAB

I was given a problem of using the following recipes to calculate how many gallons of blend could be produced.

1 gallon orange blend: 3 quarts of orange juice, 0.75 quart of pineapple juice, 0.25 quart of mango juice.

1 gallon pineapple blend: 1 quart of orange juice, 2.5 quarts of pineapple juice, 0.5 quart of mango juice.

1 gallon mango blend: 0.5 quart of orange juice, 0.5 quart of pineapple juice, 3 quarts of mango juice.

You are given 7600 gallons of orange juice, 4900 gallons of pineapple juice, and 3500 mango juice

I converted all of the recipe requirements to gallons

Here's my code but it is not giving me a straightforward answer. Why is it giving me odd decimal answers?

clc
clear

 A = [.75;.1875;.0625];

 B = [.25;.625;.125];

 C = [.125;.125;.75];

 X = [7600;4900;3500];

 OrangeBlend = X./A

 PineappleBlend  = X./B

 MangoBlend = X./C

Upvotes: 0

Views: 387

Answers (1)

reverse_engineer
reverse_engineer

Reputation: 4269

I think this is meant to be an optimization problem: You want to maximize the amount of blend you make with the available juices you have:

Amount of blend:

max blendorange + blendpineapple + blendmango

with

0.75*blendorange + 0.25*blendpineapple + 0.125*blendmango < 7600;
0.1857*blendorange + 0.625*blendpineapple + 0.125*blendmango < 4900;
0.0625*blendorange + 0.125*blendpineapple + 0.75*blendmango < 3500;

This translates in Matlab in a linprog problem:

f = [-1 -1 -1]'; % because linprog minimizes and we want to maximize
A = [0.75 0.25 0.125;0.1875 0.625 0.125;0.0625 0.125 0.75];
b = [7600;4900;3500];
linprog(f,A,b)

This gives:

ans =

  1.0e+003 *

    8.0000
    4.8000
    3.2000

So 8000 gallons of orange, 4800 gallons of pineapple and 3200 gallons of mango...

Funny to notice is that 

A*ans

yields 1.0e+003 *

    7.6000
    4.9000
    3.5000

So exactly all the juices are used. This means the problem could just have been solved with:

A\b

because the proportions are exactly so that when maximizing the blend quantity you use up all the juice. Anyway I don't know how the question was asked to you so that's why I didn't go for the linear equation directly.

Hope this helps...

Upvotes: 2

Related Questions