[Chapter 13] Integer Linear Optimization Models

The Emerald Investment Group is considering investing in six projects. The expected net present value (NPV) and the required capital at the present time for each project are given in the table below.

Project	Expected NPV ($)	Required Capital ($)
1	6,000	5,000
2	8,000	7,000
3	3,000	2,000
4	5,000	4,000
5	7,000	6,000
6	4,000	3,000

At present, a budget of $21,000 is available for investment. Emerald has specific requirements for the investment, as detailed in the Constraints section given below.

Please help Emerald develop an investment plan by formulating an integer linear optimization model.

I. Define the decision variables.

(Note: This step is done for you. Please use these decision variables hereafter.)

X₁ = 1 if project 1 is selected for investment; 0 otherwise.

X₂ = 1 if project 2 is selected for investment; 0 otherwise.

X₃ = 1 if project 3 is selected for investment; 0 otherwise.

X₄ = 1 if project 4 is selected for investment; 0 otherwise.

X₅ = 1 if project 5 is selected for investment; 0 otherwise.

X₆ = 1 if project 6 is selected for investment; 0 otherwise.

What is the objective?

Question 9 options:

	Max Z = 5,000 X1 + 7,000 X2 + 2,000 X3 + 4,000 X4 + 6,000 X5 + 3,000 X6
	Min Z = X1 + X2 + X3 + X4 + X5 + X6
	Min Z = 6,000 X1 + 8,000 X2 + 3,000 X3 + 5,000 X4 + 7,000 X5 + 4,000 X6
	Max Z = X1 + X2 + X3 + X4 + X5 + X6
	Min Z = 5,000 X1 + 7,000 X2 + 2,000 X3 + 4,000 X4 + 6,000 X5 + 3,000 X6
	Max Z = 6,000 X1 + 8,000 X2 + 3,000 X3 + 5,000 X4 + 7,000 X5 + 4,000 X6

Question 10 (2 points)

Among projects 1, 3, and 4, two of them must be selected.

Question 10 options:

	X1 + X3 + X4 < 2
	X1 + X2 + X3 + X4 + X5 + X6 = 2
	X1 + X3 + X4 > 2
	X1 + X3 + X4 2
	X1 + X3 + X4 2
	X1 + X3 + X4 = 2