# solution

1. Formulate a linear programming model using the â€œProblem statementâ€ and â€œDescription of decision variablesâ€ given in Part A.

provide the full model formulation, including:

• List of decision variables and their descriptions
• Objective function formulation
• Complete list of constraint formulations, both operational constraints and constraints on decision variables

three ingredients are used in making a pet food. Each of these nutrients have three essential nutrients. The objective of the problem is to design a daily diet by mixing these three ingredients at minimum cost, while satisfying the daily requirement of the essential nutrients.

The cost per pound of each ingredient is 300, 200 and250 cents respectively

Ingredient 1 contains 4, 9 and 10 units of nutrient A, B, and C respectively

Ingredient 2 contains 1, 1 and 40 units of nutrient A, B, and C respectively

Ingredient 3 contains 3, 4 and 3 units of nutrient A, B, and C respectively

Daily nutritional requirement is 6, 10 and 20 units of nutrient A, B and C respectively

X1 : quantity (lbs) of ingredient 1 to be mixed in the daily diet

X2 : quantity (lbs) of ingredient 2 to be mixed in the daily diet

X3 : quantity (lbs) of ingredient 3 to be mixed in the daily diet

Problem statement: The problem statement in this case is to minimize the total cost incurred for each pound of ingredient for the producer.

The variables in this case is the quantity of each pound of ingredient produced. Let the variables X1, X2 and X3 represent the three nutrients respectively.

The objective function would be:

Minimize Z= 300 X1 + 200 X2 + 250 X3

Subject to constraints

4 X1 + X2 + 3 X3 = 6 (Variable for ingredient 1)

9 X1 + X2 + 4 X3 = 10 (Variable for ingredient 1)

10 X1 + 40 X2 + 3 X3 = 20 (Variable for ingredient 1)

X1,X2, X3 = 0