# Linear Programming

• May 22nd 2007, 11:17 AM
clarson01-25@comcast.net
Linear Programming
HERE'S THE PROBLEM HELP ME SOLVE IT

A HOSPITAL IS TO ARRANGE A SPECIAL DIET COMPOSED OF TWO BASIC FOOD GROUPS FOOD A AND FOOD B. EACH OUNCE OF FOOD a HAS 30 UNITS OF CALCIUM,10 UNITS OF PROTEINAND 200 MG OF FAT. EACH OUNCE OF FOOD B HAS 20 UNITS OF CALCIUM,20 UNITS OF PROTEIN AND 150 MG OF FAT THE DIET IS TO INCLUDE AT LEAST 360 UNITS OF CALCIUM AND AT LEAST 240 UNITS OF PROTEIN.
hOW MANY OUNCES OF EACH FOOD MUST BE USED TO MEET THE CALCIUM AND PROTEIN REQUIREMENTS AND AT THE SAME TIMEMINIMZE FAT?
and if the fat in eachounce of food b decreased to 100mg how many ounces of each type of food should be used to meet the diet requirements while minimzing the amount of fat?:confused:
• May 22nd 2007, 12:25 PM
janvdl
The Equation for the calcium graph is:

$30x + 20y >= 360$

The Equation for the protein graph is:
$10x + 20y >= 240$

The Equation for the fat graph is:
$Fat = 200x + 150y$

$y = \frac{Fat}{150} - \frac{4x}{3}$

Now just draw your graph. :)
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For 100 mg Fat in B:
$y = \frac{Fat}{100} - 2x$

Hope this helps! :)

Oh, by the way, in the formulas for calcium and protein, work towards y, like we did in the fat equations.