SOLUTION: A cat breeder has the following amounts of cat food: 120 units of tuna, 110 units of liver, and 70 units of chicken. To raise a Siamese cat, the breeder must use 2 units of tuna,

Question 1143452: A cat breeder has the following amounts of cat food: 120 units of tuna, 110 units of liver, and 70 units of chicken.
To raise a Siamese cat, the breeder must use 2 units of tuna, 2 of liver and 3 of chicken, while raising a Persian cat requires
3, 2, and 1 units respectively per day.
If a Siamese cat sells for $14 and a Persian cat sells for $16, how many of each
should be raised in order to obtain maximum gross income?

Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
A cat breeder has the following amounts of cat food: 120 units of tuna, 110 units of liver, and 70 units of chicken.
To raise a Siamese cat, the breeder must use 2 units of tuna, 2 of liver and 3 of chicken, while raising a Persian cat requires
3, 2, and 1 units respectively per day.
If a Siamese cat sells for $14 and a Persian cat sells for $16, how many of each
should be raised in order to obtain maximum gross income?
Set up the system of equations and initial simplex tableau.

Let x = no. of Siamese cats to be raised
Let y = no. of Persian cats to be raised
We make the tuna inequality to make sure we don't run out of tuna,

We make the liver inequality to make sure we don't run out of liver.

We make the chicken inequality to make sure we don't run out of chicken.

We make the objective equation for the income that we want to maximize.
P = 14x + 16y
So We add NOB-NEGATIVE slack variables to take up the slack and turn the 3
inequalities into equations:



Then we rearrange the objective equation so that the variable terms are
negative and we have 0 on the right:

So we have this system of equations:


We make the augmented matrix for the system:




I'm going to stop here.  If you need help finishing,
tell me so in the form below, and I'll get back to
you by email. No charge.  I'm an 82-year-old retired
math professor, and I just do this for fun. lol

Edwin

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