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 in the following table. The nutritional requirements are as follows. The beverage must total at least 400 calories. No more than 30 percent of the total calories should come from fat. There must be at least 50 milligrams (mg) of vitamin content. For taste reasons, number of tablespoons (tbsp.) of strawberry flavoring must be greater than or equal to that of the artificial sweetener plus one. 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.
a. Write the mathematical model for this problem. [You should define the decision variables first, and then write the objective function and constraints. The objective function and constraints in the mathematical model should be numbered, and you should explain each of them after the mathematical model by referring to their number.]
b. Report the screenshot of the spreadsheet model of this problem in which the optimal solution can be seen as well.
c. Interpret the optimal solution (what do you suggest to the manager?).