Question: The following Linear Program was developed. X 1 : Pounds of ingredient 1 in product X X 2 : Pounds of ingredient 2 in product
- The following Linear Program was developed.
X1: Pounds of ingredient 1 in product X X2: Pounds of ingredient 2 in product X
X3: Pounds of ingredient 3 in product X Y1: Pounds of ingredient 1 in product Y
Y2: Pounds of ingredient 2 in product Y Y3: Pounds of ingredient 3 in product Y
Z1: Pounds of ingredient 1 in product Z Z2: Pounds of ingredient 2 in product Z
Z3: Pounds of ingredient 3 in product Z
Max profit = 2X1 + 3X2 + 5X3 + 1Y1 + 4Y2 + 2Y3 + 3Z1 + 1Z2 + 2Z3
Constraints: Max of Ingredient 1 in product X X1 0.3 (X1 + X2 + X3)
Min of Ingredient 2 in product X X2 0.2 (X1 + X2 + X3)
Min of Ingredient 3 in product Y Y3 0.3 (Y1 + Y2 + Y3)
Max of Ingredient 2 in product Z Z2 0.4 (Z1 + Z2 + Z3)
Max of Ingredient 1 in pounds X1 + Y1 + Z1 5000
Max of Ingredient 2 in pounds X2 + Y2 + Z2 5000
Max of Ingredient 3 in pounds X3 + Y3 + Z3 5000
Max of product Z Z1 +Z2 + Z3 0.2(X1 +X2 + X3 +Y1 + Y2 +Y3 + Z1 + Z2 + Z3)
All variables non-negative
- Solve the LP problem using solver and write the strategy (HINT: be sure that all the constraints are in standard format) (60 pts)
- Run a sensitivity analysis and identify the binding constraints (20 pts)
- What is the change in the objective function value if 1000 more pounds of each of Ingredient 1, 2, and 3 were available? (10 pts)
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