Posted: February 7th, 2016

Hot Dog Mix Planning – Linear Programming

A meatpacking house is creating a new variety of hot dog for the low-calorie, low-fat, low-cholesterol market. This new hot dog will be made of beef and pork, plus either chicken, turkey, or both. It will be marketed as a 2-ounce all-meat hot dog, with no fillers. Also, it will have no more than 6 grams of fat, no more than 27 grams of cholesterol, and no more than 100 calories. The cost per pound for beef, pork, chicken, and turkey, plus their calorie, fat, and cholesterol counts, are shown in the following table.

Cost/Pound Calories/Pound Fat (G/lb) Cholesterol (G/lb)
Beef $ 0.76 640 32.5 210
Pork $ 0.82 1055 54 205
Chicken $ 0.64 780 25.6 220
Turkey $ 0.58 528 6.4 172

The packer would like each 2-ounce hot dog to be at least 25% beef and at least 25% pork.
Solve the given problem scenario for the meatpacking house by recommending the most economical combination of four meats to make this hot dog. Formulate and set up the problem using the most appropriate technique in Excel Solver