## 9:30 AM Class Group 5

Leo Carey
Ryan McNally
Eric Demmons
Igli Cyreku
Mike Bogush

Problem: Suppose the only foods available in your local supermarket are meat and potatoes. Suppose each portion of potatoes contains 3 units of carbohydrates, 4 units of vitamins, 1 unit of protein and costs 75 cents, while each portion of meat contains 1 unit of carbohydrates, 3 units of vitamins, 3 units of protein and costs 2 dollars. Suppose also a balanced diet requires a daily minimum of 8 units of carbohydrates, 19 units of vitamins and 7 units of protein.

Given the economy, you are greatly concerned about meeting your own minimum daily requirements while spending as little as possible.

Your task at the moment is to model this problem algebraically. You are to clearly define appropriate variables and represent each of the constraints (conditions) as well as the total amount you will be spending in terms of those variables. You do not need to solve the problem at this time; you merely need to set up a model.

Let x be the amount of potatoes required to fulfill daily dietary requirements.
Let y be the amount of meat required to fulfill daily dietary requirements.
Let m be the minimum cost to fulfill daily dietary requirements.
 Food Carbs Vitamins Protein Cost/per unit Potatoes3 4 1 \$ 0.75 Meat 1 3 3 \$ 2.00 Daily Requiremnets 8 19 7 m=.75x+2y
Constraints:
3x+y≥8 Carbohydrates
4x+3y≥19 Vitamins
x+3y≥7 Protein

Non-negativity conditions:
x≥0, y≥0

Objective Sum Function:
m=.75x+2y

The equation 3x+y≥8 represents the amount of meat(y) and potatoes(x) to fulfill the daily dietary requirements for carbohydrates.

The equation 4x+3y≥19 represents the amount of meat(y) and potatoes(x) to fulfill the daily dietary requirements for vitamins.

The equation x+3y≥7 represents the amount of meat(y) and potatoes(x) to fulfill the daily dietary requirements for protein.

The equations x≥0 and y≥0 represents the fact you cannot have a negative amount of meat(y) or potatoes(x).

The equation m=.75x+2y represents the minimum cost(m) for meeting the daily dietary requirements of carbohydrates, vitamins, and proteins received from meat(y) and potatoes(x).