3. Develop the complete model, clearly showing the decision variables, objective

Question

3. Develop the complete model, clearly showing the decision variables, objective function, and all constraints very clearly (assume the reader doesn't know much) roblem 1: Wendy loves steaks and potatoes. Therefore, she has decided to go on a steady diet of only these two foods (plus some liquid and vitamin supplements) for all of her meals. Wendy realizes that this isn't the healthiest diet, so she wants to make sure that she eats the right quantities of the two foods to satisfy some key nutritional requirements. She has obtained the following nutritional and cost information: Grams of Ingredient per Serving Daily Requirement Steak (grams) e 50 2 40 S 60 Potatoes Ingredient Carbohydrates Protein Fat Cost per Serving (S) 15 Wendy wishes to determine the number of daily servings (may be fractional) of steak and potatoes that will meet these requirements at a minimum cost. Develop a linear programming model that will be used to solve the problem

Explanation / Answer

In the given scenario:

Decision Variables

Let x be the No. of Steaks and

y be the No. of Potatoes

Objective Function

The Objective is to minimize the Total Cost.

Let Z be the Objective Function.

So the Objective Function can be written as:

Minimize Z = 4x + 2y

Constraints

For Carbohydrates:

5x + 15y >= 50

For Protein:

20x + 5y >= 40

For Fats:

15x + 2y <= 60

Non-Negativity Constraint:

x >= 0

y >= 0

Required Linear Programming Model

Minimize Z = 4x + 2y

Subject to:

5x + 15y >= 50

20x + 5y >= 40

15x + 2y <= 60

x >= 0

y >= 0

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