Ima Hogg wants to determine the quantity of ingredients to use in making each pound of sausage at a minimum cost. The available ingredients and their relevant data are: Hog bellies cost $.30, and contain 3 ounces of protein, 5 ounces of fat, and 6 ounces of water; Tripe costs $.20, contains 5 ounces of protein, 3 ounces of fat, and 4 ounces of water; Beef costs $.70, contains 4 ounces of protein, 2 ounces of fat, and 5 ounces of water; Pork costs $.60, contains 3 ounces of protein, 4 ounces of fat, and 9 ounces Ima must meet the specified weight exactly, and there are further restrictions. No more than 10% of the sausage weight can be composed of hog bellies and chicken cannot exceed 25% of total content, and at least 30% of the sausage must be beef. In addition, a minimum of 3 ounces of protein must be present in each pound of sausage. Furthermore, each pound of sausage may contain a maximum of 4 ounces of fat and maximum of 8 ounces of water.
a. Formulate the problem as a linear program. Identify the objective function, decision variables, constraints and any other necessary information.
b. Use excel to display the linear program.
c. Use excel to find the optimal solution
1. What is the optimal Solution?
2. Which variable have slack?
3. Which are binding?