2. Ethelred’s new Mediterranean diet requires that all his food come from one of

Question

2. Ethelred’s new Mediterranean diet requires that all his food come from one of the four “basic food groups”, namely, Greek salad, figs, red wine, and chocolate. Each serving of Greek salad costs $6, each bag of figs costs $2, each bottle of red wine costs $3, and each bar of chocolate costs $7. Each day, Ethelred must ingest at least 800 calories, at least 8 units of nutrient 1, at least 12 units of nutrient 2, and at least 10 units of nutrient 3. The nutritional content per unit of each food is given below:

Calories

Nutrient 1

Nutrient 2

Nutrient 3

Greek Salad (GS)

400

3

2

2

Figs (FG)

200

2

2

4

Red Wine (RW)

150

0

4

1

Chocolate (CH)

500

0

4

5

i) Formulate an LP problem to help Ethelred to minimize his daily food costs. (Be sure to define the decision variables, state the objective function, state and label the constraints, and include the sign restrictions.)

Calories

Nutrient 1

Nutrient 2

Nutrient 3

Greek Salad (GS)

400

3

2

2

Figs (FG)

200

2

2

4

Red Wine (RW)

150

0

4

1

Chocolate (CH)

500

0

4

5

Explanation / Answer

Decision variables,

Here the decision variables are defined as the number of units for each of the 4 types of food items that are: GS, FG, RW and CH.

Therefore the decision variables here would be given as: X1, X2, X3 and X4

Constraints:

Here we are given the constraints for the number of nutrients of each of the 3 types and also the calories. These constraints would be given as:

Objective function:

Minimizing the cost of the units purchased. This would be given as:

Min the function : 6X1 + 2X2 + 3X3 + 7X4

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