Slim-Down Manufacturing makes a line of nutritionally complete, weight-reduction beverages. One of their products is a strawberry shake which is designed to be a complete meal. The strawberry shake consists of several ingredients. Some information about each of these ingredients is given below. Take the ingredient of strawberry flavoring for example, the amount of calories from fat of each unit (tbsp) of strawberry flavoring is 1, the amount of total calories from each unit of strawberry flavoring is 50, similarly, the amount of vitamin content and thickeners is 20mg and 3mg per tbsp. The cost of each tbsp of strawberry flavoring is 10 dollars.

Ingredient

Calories from Fat

(per/tbsp)

Total Calories

(per/tbsp)

Vitamin Content

(mg/tbsp)

Thickeners

(mg/tbsp)

Cost

($/tbsp)

Strawberry flavoring

1

50

20

3

10

Cream

38

112

0

15

5

Vitamin supplement

0

0

50

1

6

Artificial sweetener

0

110

0

3

4

Thickening agent

12

60

2

15

9

The nutritional requirements are as follows. There must be at least 20 milligrams (mg) of vitamin content. For taste reasons, there must be at least 4 tablespoons (tbsp) of strawberry flavoring for each tablespoon of artificial sweetener. To maintain proper thickness, there must be exactly 20 mg of thickeners in the beverage. Finally, the beverage must total between 300 and 400 calories (inclusive), and no more than 30 percent of the total calories should come from fat.

Management would like to select the quantity of each ingredient for the beverage which would minimize cost while meeting the above requirements.

Please formulate a linear programming model for this problem.