Use R Studio

Below there is a diet chart which gives calories, protein, carbohydrate and fat content for 4 food items. Sara wants a diet with minimum cost. The diet chart is as follows:

	Food Item 1	Food Item 2	Food Item 3	Food Item 4
Calories	400	200	150	500
Protein (in grams)	3	2	0	0
Carbohydrates ( in grams)	2	2	4	4
Fat (in grams)	2	4	1	5
Cost	$1.00	$0.40	$0.60	$1.80

The chart gives the nutrient content as well as the per-unit cost of each food item. The diet has to be planned in such a way that it should contain at least 500 calories, 6 grams of protein, 10 grams of carbohydrates and 8 grams of fat.

Determine how much of each food item is to be used in the diet to minimize the total cost.

Use the notebook homework7Pr2.Rmd file posted on Sakai for this problem.

Formulate the linear programming model for this problem.

Define the decision variables

Formulate the objective function

State the constraints

Entering the problem data and finding the optimum solution using R Studio

Call lpSolve library Library (lpSolve)

Enter the problem Data (formulation)

Solution - Solve the problem

Display the optimum solution values? How much of each food item should be used in the diet?

Display the objective function value (total cost) of the optimum solution? What is the total cost?

Obtain the dual values.

What are the dual values for the calorie, protein, carbohydrate, and fat requirements?

How much would the cost increase if the diet required one additional gram of calorie (501 grams instead of 500)?