My diet requires that all food I eat come from one of the four \"basic food grou

Question

My diet requires that all food I eat come from one of the four "basic food groups" (choolcate cake, ice cream, soda and cheesecake) At present, the following four foods are available for consumption: brownies, chocolate ice cream, cola, and pineapple cheesecake. Each brownie cost 50cents, each scoop of ice cream cost 20cents, each bottle of cola cost 30 cents and each piece of pineapple cheesecake cost 80 cents. Each day, I must ingest 500 calories, 6 oz of chocoloate, 10 oz of sugar, and 8 oz of fat. The nutrictional content per unit of each food is shown in the following tabel. Formulate a linear programming model that can be used to satisfy my dayily nutritional requirements at minimual cost.

Type

Calories

Chocolate (oz)

Sugar (oz)

Fat (oz)

Brownie

400

3

2

8

Chocolate Ice Cream

200

2

2

4

Cola

150

0

4

1

Pineapple Cheesecake

500

0

4

5

1. Formulate a linear porgramming model for this problem by:

listing and labeling all of the decision variables

creating an objective function for the model

liss all of the contstrains for the model

Solve the model using Excel solver. Give the value for each decision variable and the objective function.

Type

Calories

Chocolate (oz)

Sugar (oz)

Fat (oz)

Brownie

400

3

2

8

Chocolate Ice Cream

200

2

2

4

Cola

150

0

4

1

Pineapple Cheesecake

500

0

4

5

Explanation / Answer

Type

Calories

Chocolate (oz)

Sugar (oz)

Fat (oz)

Brownie

400

3

2

8

Chocolate Ice Cream

200

2

2

4

Cola

150

0

4

1

Pineapple Cheesecake

500

0

4

5

let x1 is the no of brownie used,

x2 ,,,, is he no of chockolate ice cream used

x3 is the no of cola used

x4 is the no of pineapple cheesecake used

so our objective function is to minimise total cost

total cost = 50x1+20x2+30x3 + 80x4

so objective function is minimise 50x1+20x2+30x3 + 80x4

and the constraints are

400x1+200x2+150x3+500x4 > or= 500

3x1+2x2> or = 6

2x1+2x2+4x3+4x4> or =10

and

8x1+4x2+x3+5x4> or= 8

also x1,x2,x 3, x4, are greater than or > 0

Type

Calories

Chocolate (oz)

Sugar (oz)

Fat (oz)

Brownie

400

3

2

8

Chocolate Ice Cream

200

2

2

4

Cola

150

0

4

1

Pineapple Cheesecake

500

0

4

5

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