Question: Minimize 300 X 1 + 200 X 2 + 250 X 3 Subject to 4 X 1 + X 2 + 3 X 3 6
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Minimize 300 X1 + 200 X2 + 250 X3
Subject to
4 X1 + X2 + 3 X3 6
9 X1 + X2 + 4 X3 10
10 X1 + 40 X2 + 3 X3 20
X1,X2, X3 0
Your answer should follow the template given below:
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
The last (non-negativity) constraint implies that the value of each decision variable must be positive.
- (5 points) Formulate a linear programming model using the Problem statement and Description of decision variables given in Part A.
To get full credit from part B, you need to 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
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