(a) Formulate this problem as an LP. Show the algebraic formulation in your submission.

(b) Input and solve this formulation using Excel. After running Solver, generate sensitivity report.

(c) Answer the following questions. Again, I do not want you to rerun more linear programs. You must answer the questions based on the one linear program solution/sensitivity report from. You must explain all the steps on how you answered the question based on the one output for the linear program. If you feel that it is not possible to answer the question with the single output, explain why this is the case.

i) In units of pounds, what are the optimal values of A, B, C?

ii) What is the minimum cost per serving of cereal?

iii) How many units of Protein, Riboflavin, Phosphorus and Magnesium are in the minimum cost serving?

iv) What will be the cost per serving if regulations now require 2.2 units of riboflavin?

v) What will be the cost per serving if only 0.5 units of phosphorus are required?

vi) What will be the cost per serving if only 0.4 units of magnesium are required?

vii) What would be the optimal values of A, B, C if the cost of grain A increases to 36? What would be the minimum cost per serving with such an increase?

viii) What would be the optimal values of A, B, C if the cost of grain C decreases to 30?

The diet problem, one of the earliest applications of linear programming, was originally used by hospitals to determine the most economical diet for patients. Known in agricultural applications as the feed mix problem, the diet problem involves specifying a food or feed ingredient combination that satisfies stated nutritional requirements at a minimum cost level. The Whole Food Nutrition Center uses three bulk grains to blend a natural cereal that it sells by the pound. The store advertises that each serving of the cereal meets an average adult's minimum requirement for protein, riboflavin, phosphorus, and magnesium. The cost of each bulk grain and the protein, riboflavin, phosphorus, and magnesium units per pound are each shown in the table below: Cost per Protein Riboflavin Phosphorus Magnesium Grain Pound (units/lb) (units/1b) (units/lb) (units/lb) A 336 22 16 8 5 B 474 28 14 7 0 380 21 25 9 6 A serving cereal must have a minimum of 3 units of protein, 2 units of riboflavin, 1 unit of phosphorus and 0.425 units of magnesium. Define, A = pounds of grain A in one servings of cereal B = pounds of grain B in one servings of cereal C = pounds of grain Cin one servings of cereal 4 One serving of cereal is 0.125 pound. So, in addition to the nutrients requirements, the sum of these three variable values must equal to the weight per serving. The diet problem, one of the earliest applications of linear programming, was originally used by hospitals to determine the most economical diet for patients. Known in agricultural applications as the feed mix problem, the diet problem involves specifying a food or feed ingredient combination that satisfies stated nutritional requirements at a minimum cost level. The Whole Food Nutrition Center uses three bulk grains to blend a natural cereal that it sells by the pound. The store advertises that each serving of the cereal meets an average adult's minimum requirement for protein, riboflavin, phosphorus, and magnesium. The cost of each bulk grain and the protein, riboflavin, phosphorus, and magnesium units per pound are each shown in the table below: Cost per Protein Riboflavin Phosphorus Magnesium Grain Pound (units/lb) (units/1b) (units/lb) (units/lb) A 336 22 16 8 5 B 474 28 14 7 0 380 21 25 9 6 A serving cereal must have a minimum of 3 units of protein, 2 units of riboflavin, 1 unit of phosphorus and 0.425 units of magnesium. Define, A = pounds of grain A in one servings of cereal B = pounds of grain B in one servings of cereal C = pounds of grain Cin one servings of cereal 4 One serving of cereal is 0.125 pound. So, in addition to the nutrients requirements, the sum of these three variable values must equal to the weight per serving