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 $15mg$ 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.

a$.$ Identify the requirements that lead to resource constraints, to benefit constraints, and to fixed$-$requirement constraints.

b$.$ Formulate and solve a linear programming model for this problem on a spreadsheet.

c$.$ Summarize this formulation in algebraic form.