Doug Turner Food Processors wishes to introduce a new brand of dog biscuits composed of chicken- and liver-flavored biscuits that meet certain nutritional requirements. The liver-flavored biscuits contain 3 units of nutrient A and 1 unit of nutrient B; the chicken-flavored biscuits contain 3 units of nutrient A and 2 units of nutrient B. According to federal requirements, there must be at least 55 units of nutrient A and 50 units of nutrient B in a package of the new mix. In addition, the company has decided that there can be no more than 20 liver-flavored biscuits in a package. If it costs 3¢ to make 1 liver-flavored biscuit and 2¢ to make 1 chicken-flavored, what is the optimal product mix for a package of the biscuits to minimize the firm’s cost? Formulate this as a linear programming problem (write out the objective function and the constraints including non-negativity constraint). Solve this problem using the corner-point method or the iso-profit/iso-cost line method, giving the optimal values of all variables What is the total cost of a package of dog biscuits using the optimal mix? Which constraints are binding? solve the question using Excel OM, Solve the same problem using excels solver using "Simplex LP" instead of the default solver "GRG nonlinear" running a sensitivity analysis and explain the shadow prices.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Doug Turner Food Processors wishes to introduce a new brand of dog biscuits composed of chicken- and liver-flavored biscuits that meet certain nutritional requirements. The liver-flavored biscuits contain 3 units of nutrient A and 1 unit of nutrient B; the chicken-flavored biscuits contain 3 units of nutrient A and 2 units of nutrient B. According to federal requirements, there must be at least 55 units of nutrient A and 50 units of nutrient B in a package of the new mix. In addition, the company has decided that there can be no more than 20 liver-flavored biscuits in a package. If it costs 3¢ to make 1 liver-flavored biscuit and 2¢ to make 1 chicken-flavored, what is the optimal product mix for a package of the biscuits to minimize the firm’s cost? Formulate this as a linear programming problem (write out the objective function and the constraints including non-negativity constraint). Solve this problem using the corner-point method or the iso-profit/iso-cost line method, giving the optimal values of all variables What is the total cost of a package of dog biscuits using the optimal mix? Which constraints are binding? solve the question using Excel OM, Solve the same problem using excels solver using "Simplex LP" instead of the default solver "GRG nonlinear" running a sensitivity analysis and explain the shadow prices.

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