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).