- 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