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. 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.

$\backslash$table$[[$Ingredient$,\backslash$table$[[$Calories from Fat$],[($per tablespoon$)]],\backslash$table$[[$Total Calories$],[($per tablespoon$)]],\backslash$table$[[$Vitamin Content$],[($mg$/$tablespoon$)]],\backslash$table$[[$Thickeners$],[($mg$/$tablespoon$)]],(\frac{\text{\$}}{?}$ tablespoon$)],[$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,$30,80,2,25,6]]$

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

a$.$ Determine the quantity of each ingredient for the beverage.

Note: Leave no cells blank. Enter $"$O$"$ when necessary. Round your answers to $3$ decimal places.