How can you express the following constraint using the decision variables defined previously?

A. If project 3 is selected, project 4 cannot be selected.

P₃ + P₄ 1

P₃ P₄

1 - P₄ P₃

1 - P₃ P₄

P₄ 1 + P₃

_B. How can you express the following constraint using the decision variables defined previously? Additional decision variables can be defined if necessary.

At most two of the investments 1, 2, 3 are chosen, or at least three of the investments 3, 4, 5, 6 are chosen.

2 - (P₁ + P₂ + P₃) M * Y, (P₃ + P₄ + P₅ + P₆) - 3 M * (1 - Y),

Y is binary, M is a large number

(P₁ + P₂ + P₃) - 2 M * Y, 3 - (P₃ + P₄ + P₅ + P₆) M * (1 - Y),

Y is binary, M is a large number

(P₁ + P₂ + P₃) 2Y, (P₃ + P₄ + P₅ + P₆) 3(1 - Y),

Y is binary

(P₁ + P₂ + P₃) 2Y, (P₃ + P₄ + P₅ + P₆) 3(1 - Y),

Y is binary

(P₁ + P₂ + P₃) 2Y, (P₃ + P₄ + P₅ + P₆) 3Y,

Y is binary

C. How can you express the following constraint using the decision variables defined previously? You may define additional decision variables if needed.

Either both investments 1 and 2 are chosen, or neither investment 5 nor 6 is chosen.

(P₁ + P₂) = M * Y, (P₅ + P₆) = M * (1 - Y),

Y is binary, M is a large number

2 - (P₁ + P₂) M * Y, (P₅ + P₆) M * (1 - Y),

Y is binary, M is a large number

2 - (P₁ + P₂) M * Y, (P₅ + P₆) M * (1 - Y),

Y is binary, M is a large number

2 - (P₁ + P₂) M * Y, (P₅ + P₆) M * (1 - Y),

Y is binary, M is a large number

(P₁ + P₂) 2Y, (P₅ + P₆) 0,

Y is binary

Capital Budgeting Company is trying to select projects that maximize the NPV. The company has $250,000 available in year 1 to invest in new projects. It has budgeted $75,000 for continued support for these projects in year 2 and $50,000 in year 3. The NPV and the annual capital required for the next three years are summarized for the projects below. Expected NPV Capital (in $000s) Required Project (in $000s) Year 1 Year 2 Year 3 1 $141 $75 $25 $20 2 $187 $90 $35 $0 3 $121 $60 $15 $15 4 $83 $30 $20 $10 5 $265 $100 $25 $20 6 $127 $50 $20 $10 To set up an integer programming model to maximize the NPV, let us define the decision variables as the following P; = 1 if project i is selected otherwise 0. i=1,2,3,4,5,6 Capital Budgeting Company is trying to select projects that maximize the NPV. The company has $250,000 available in year 1 to invest in new projects. It has budgeted $75,000 for continued support for these projects in year 2 and $50,000 in year 3. The NPV and the annual capital required for the next three years are summarized for the projects below. Expected NPV Capital (in $000s) Required Project (in $000s) Year 1 Year 2 Year 3 1 $141 $75 $25 $20 2 $187 $90 $35 $0 3 $121 $60 $15 $15 4 $83 $30 $20 $10 5 $265 $100 $25 $20 6 $127 $50 $20 $10 To set up an integer programming model to maximize the NPV, let us define the decision variables as the following P; = 1 if project i is selected otherwise 0. i=1,2,3,4,5,6