$\backslash$table$[[$Ingredient$,\backslash$table$[[$Fat $($per$],[$tbsp$.)]],\backslash$table$[[$Calories$],[($per tbsp$.)]],\backslash$table$[[$Content$],[($mg$/$tbsp$.)]],\backslash$table$[[$Thickeners$],[($mg$/$tbsp$.)]],\backslash$table$[[$Cost$],[(\frac{\text{\$}}{?}$ tbsp$.)]]],[\backslash$table$[[$Strawberry$],[$flavoring$]],1,50,20,3,10],[$Cream$,75,100,0,8,8],[\backslash$table$[[$Vitamin$],[$supplement$]],0,0,50,1,25],[\backslash$table$[[$Artificial$],[$sweetener$]],0,120,0,2,15],[\backslash$table$[[$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 $15mg$ of thickeners in the beverage.

Management,would like to select the quantity of each ingredient for the beverage that

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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.