Capital Project Knapsack You have the following capital project with different c

Question

Capital Project Knapsack You have the following capital project with different costs and value. You have a total project budget of 10 M. Develop a formulation to maximize the value of the project minus the cost of the projects. Project Cost (m) Value 1.1 2.1 1.2 4 1.5 2.2 1.8 .4 4.1 10 5.9 10 a. Formulate this problem (15 points) b. Management suggests that you can only do 6 projects in a time period due to management time constraints. Add this constraint to your formulation. c. Only project 1 or 2 can be performed but not both. Add this constraint. d. Project 7 cannot be done unless project 6 is done?

Explanation / Answer

a) Formulation:

Let Xi be a binary variable such that Xi =1 represent that project i is done, otherwise not.

Max (1.1-1)X1+(3-2.1)X2+(1.2-0.5)X3+(0.6-0.3)X4+(0.2-1.5)X5+(4.1-2.2)X6+(2-1.8)X7+(0.5-0.4)X8+(2-0.8)X9+(10-5.9)X10

s.t.

1X1+2.1X2+0.5X3+0.3X4+1.5X5+2.2X6+1.8X7+0.4X8+0.8X9+5.9X10

Xi {0,1}

b) This constraint is as below

X1+X2+X3+X4+X5+X6+X7+X8+X9+X10 <= 6

c) This constraint is as below

X1+X2 <= 1

d) This constraint is as below

X6 - X7 >= 0

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