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Question: a daily diet should contain at least 400 units of...

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A daily diet should contain at least 400 units of carbohydrates, 50 units of fat and 30 units of protein. Two foods sources, say A and B, are available. Food source A costs 2 dollars per unit and food source B costs 4 dollars per unit. A unit of food source A contains 1 unit of carbohydrates, 2 units of fat and 1.5 units of protein. A unit of food B contains 2.5 units of carbohydrates, 1 unit of fat and 2 units of protein.

A) Formulate the math programming model to find the minimum cost for a diet that consists of a mixture of the two type foods and also meets the minimum daily nutrition requirements. Explicitly state your decision variables and write the mathematical models for the objective function and constraints.

B) Implement the model in Excel.

C) Use the Excel solver to find the optimal solution to the problem.

D) Perform a sensitivity analysis to answer the following questions.

  • If you are allowed to reduce the minimum daily requirement of only one nutrient- carbohydrates, fat, or protein- one unit, which one would you choose to do so? Justify your answers.
  • What is the price level of Food type A such that the diet will only be based on Food type A?
  • What is the price level of Food type B such that the diet will only be based on Food type B?
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