The Fido Dog Food Company wishes to introduce a new brand of dog biscuits (composed of chicken and liver-flavored biscuits) that meets certain nutritional requirements. The liver-flavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B, while the chicken-flavored ones contain 1 unit of nutrient A and 4 units of nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and 60 units of nutrient B in a package of the new mix. In addition, the company has decided that there can be no more than 15 liver-flavored biscuits in a package. If it costs 1 cent to make a liver-flavored biscuit and 2 cents to make a chicken-flavored one, what is the optimal product mix for a package of the biscuits in order to minimize the firm's cost? (a) Formulate this as a linear programming problem (b) Find the optimal solution for this problem graphically (c) Are any constraints redundant? If so, which one or ones? (d) What is the total cost of a package of dog biscuits using the optimal mix?

The Fido Dog Food Company wishes to introduce a new brand of dog biscuits (composed of chicken and liver-flavored biscuits) that meets certain nutritional requirements. The liver-flavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B, while the chicken-flavored ones contain 1 unit of nutrient A and 4 units of nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and 60 units of nutrient B in a package of the new mix. In addition, the company has decided that there can be no more than 15 liver-flavored biscuits in a package. If it costs 1 cent to make a liver-flavored biscuit and 2 cents to make a chicken-flavored one, what is the optimal product mix for a package of the biscuits in order to minimize the firm's cost? (a) Formulate this as a linear programming problem (b) Find the optimal solution for this problem graphically (c) Are any constraints redundant? If so, which one or ones? (d) What is the total cost of a package of dog biscuits using the optimal mix?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 65P

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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 1 unit of nutrient A and 2 units of nutrient B; the chicken flavored biscuits contain 1 unit of nutrient A and 4 units of nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and 60 units of nutrient B in a package of the new mix. In addition, the company has decided that there can be no more than 12 liver flavored biscuits in a package. It costs 1¢ to make 1 liver flavored biscuit and 2¢ to make 1 chicken flavored. Doug wants to determine the optimal product mix for a package of the biscuits to minimize the firm's cost. The aim of the objective function should be to (Maximize or Minimize) the objective value.
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 1 unit of nutrient A and 2 units of nutrient B; the chicken flavored biscuits contain 1 unit of nutrient A and 4 units of nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and 60 units of nutrient B in a package of the new mix. In addition, the company has decided that there can be no more than 16 liver flavored biscuits in a package. It costs 1¢ to make 1 liver flavored biscuit and 2¢ to make 1 chicken flavored. Doug wants to determine the optimal product mix for a package of the biscuits to minimize the firm's cost. The aim of the objective function should be to Minimize the objective value. The optimum solution is: Number of liver flavored biscuits in a package = nothing (round your response to two decimal places).
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…
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