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.
Food
Carbohydrates
Vitamins
Proteins
Cost of One Portion of Food
Meat
1 unit
3 units
3 units
$2.00
Potatoes
3 units
4 units
1 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.