8:00 AM Class Group 2
Meat and Potatoes Group Project
Due: 01 December 2008
Group 2: Michelle Gravel, Karen Carlson, Brandon Sweet, Lindsay
Bissonnette, and Agne Bileviciute
Refer to printed copy for table.
Let the variable x stand for the number of portions of potatoes daily.
Let the variable y stand for the number of portions of meat daily.
Let the variable c stand for the total cost of diet.
The constraints are:
Units of carbohydrates: 3x + y ≥ 8
Units of vitamins: 4x + 3y ≥ 19
Units of Protein: x + 3y ≥ 7
The non-negativity conditions are:
x ≥ 0, y ≥ 0
The objective function is:
C = .75x + 2.00y
The objective of this project is to successfully create a daily balanced
diet while keeping the cost at a minimum. To achieve this goal you must
take in the proper portion of meat and potatoes. The constraints
modeled above illustrate the correct amount of potatoes and meat needed
to achieve the daily requirements of carbohydrates, vitamins, and
protein. For instance, you would need "x" amount of potatoes and "y"
amount of meat to reach a balanced diet on a daily basis. You would need
a minimum of eight units of carbohydrates, nineteen units of vitamins,
and seven units of protein.
The non-negativity conditions show the obvious concept that it is
impossible to take in a negative amount of potatoes or meat. This is
why the non-negativity conditions are "x ≥ 0" and "y ≥ 0."
However, it is possible not to take in any meat or potatoes, which is
why "x" and "y" have to be greater than or equal to zero.
The objective function's purpose is to setup daily balanced diet
requirements, while maximizing the portions of potatoes and meat, and
minimizing the cost. Each portion of potatoes would cost $0.75, and each
portion of meat would cost $2.00. By using the constraints, which help
to figure out how much meat and potatoes are needed to meet the daily
balanced requirements, you can then take the "x" amount of potatoes
and "y" amount of meat and substitute them into the objective function
equation to find out the cost. When all of this is considered we came up
with the equations depicted above.