Slim-Down Manufacturing makes a line of nutritionally complete, weight-reduction beverages. One of its products is a strawberry shake that is designed to be a complete meal. The strawberry shake consists of several ingredients. Some information about each of these ingredients is given next.

Ingredient	Calories from Fat (per tbsp.)	Total Calories ries (per tbsp.)	Vitamin Content (mg/tbsp.)	Thickeners (mg/tbsp.)	Cost (/tbsp.)
Strawberry flavoring	1	50	20	3	10
Cream	75	100	0	8	8
Vitamin supplement	0	0	50	1	25
Artificial sweetener	0	120	0	2	15
Thickening agent	30	80	2	25	6

The nutritional requirements are as follows. The beverage must total between 380 and 420 calories (inclusive). No more than 20 percent of the total calories should come from fat. There must be at least 50 milligrams (mg) of vitamin content. For taste reasons, there must be at least two tablespoons (tbsp.) of strawberry flavoring for each tbsp. of artificial sweetener. Finally, to maintain proper thickness, there must be exactly 15 mg of thickeners in the beverage.

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

1. Identify the requirements that lead to resource constraints, to benefit constraints, and to fixed-requirement constraints.
2. Formulate and solve a linear programming model for this problem on a spreadsheet.
3. Summarize this formulation in algebraic form.