8 AM Class Group 3

Anthony Calandro, Kevin Daigle, Alyssa Huddleston, Sara Lima, Daniel Marcil, Maxim Shorey
Math 1070Q
1 December, 2008
Linear Equations Project

The only foods available in our local supermarket are meat and potatoes.

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. Also a balanced diet requires a minimum of 8 units of carbohydrates, 19 units of vitamins and 7 units of protein.

The price for a portion of meat is $2 and the price for a portion of potatoes is 0.75ยข.
FoodCarbohydratesVitaminsProteinsCost of One Portion of Food
Meat1 unit3 units3 units$2.00
Potatoes3 units4 units1 unit$0.75
Unfortunately the economy is in horrible shape and spending more money than needed is a large concern. As consumers we are trying to conserve money but also have a great concern about meeting our own minimum daily requirements. So we are setting up a model to identify the cheapest possible amount of meat and potatoes we can buy while still having enough to meet our daily nutritional requirements.

Let X represent the number of portions of potatoes, and let Y represent the number of portions of meat. The constraints for each variable are X ≥ 0 and Y ≥ 0. This shows that as a consumer we will need at least zero or more portions of both meat and potatoes.

Minimum amount of each requirement shown through inequalities:

Carbohydrates: 3x + y ≥ 8 Vitamins: 4x + 3y ≥ 19 Proteins: x + 3y ≥ 7

-The objective function cost in terms of x (0.75) y (2.00).

Cost= 0.75x + 2y x=number of portions of potatoes
y=number of portions of meat

These algebraic models can be used to solve for the amount of X and Y which would show us our minimum daily requirement of meat and potatoes along with the price.