Math Fights Hunger Project
AMTEM
Name:
As a research team for the World Health Organization, you need to determine an optimal food program
for the country you have chosen. In particular, you need to minimize the total number of calories a
child consumes while meeting the requirements for key nutrients, using the highest nutrient
concentrated food combinations available in the country.
1. Define your six decision variables. The quantities that your team has control over are the
amounts of the six different foods.
2. The goal is to minimize calories. Write the equation for the objective function using your
decision variables and the data you’ve collected regarding calories.
3. How do you think this minimization problem will differ from the maximization problems that we
have solved in the previous unit?
4. Why would we want to minimize calories?
It is important that your optimal food program represent a balanced diet. The table below shows the
minimum and maximum number of calories children should consume for each food group.
Food Group
Minimum Maximum
Cereals
900
1100
Fruits
15
45
Legumes
45
150
Fish, meat, eggs
30
90
Roots
60
240
Vegetables
15
45
5. Write an inequality that represents the minimum number of calories that are recommended for
the cereal in your food program. You’ll need to multiply the number of calories for your cereal
by the variable assigned to represent your cereal and set it greater than or equal to 900.
6. Write an inequality that represents the maximum number of calories that are recommended for
the cereal in your food program.
There will be two inequalities similar to these for each of the other foods in your program. That is, there
will be 12 different constraints relating to the minimum and maximum amount of energy from those
foods.
There will also be inequalities representing the constraints for the minimum amount of nutrient the
children need in their diets. The allowances for each of the key nutrients are listed in the table below.
Nutrient
Minimum Daily Requirement
Protein
20 grams (g)
Calcium
400 milligrams (mg)
Iron
7 mg
Folate (Vit. B9)
50 micrograms (µg)
Cobalamin (Vit. B12)
0.5 µg
Ascorbic Acid (Vit. C)
20 mg
Thiamine (Vit. B1)
0.7 mg
Riboflavin (Vit. B2)
1.1 mg
Niacin (Vit. B3)
12.1 mg
Retinol (Vit. A)
400 µg
7. Consider the data you collected for the total amount of protein in each of the six foods. Write an
expression to represent how much protein will be used in a particular combination of foods. The
expression will need to be set greater than or equal to 20.
8. Now consider the data you collected for the total amount of calcium in each of the six foods.
Write an inequality to represent the constraint for the minimum amount of calcium needed in a
child’s diet.
There will be 8 more constraints for each of the remaining nutrients. Combined with the other
constraints relating to the minimum and maximum energy requirements, there will be a total of 22
constraints!
Using the partial Excel template provided, enter in all of your data, objective function, and constraints
into the spreadsheet. Then, use the Solver tool to attempt to determine the optimal food program that
will minimize calories.
9. Was Solver able to determine a solution? If so, what is the optimal plan?