Globex Investment Capital Corporation owns six companies that have the following estimated returns (in millions of dollars) if sold in 1 of the next 3 years:

Year Sold (estimated return, $1,000,000s)
Company
1
2
3
1
$14
$18
$23
2
9
11
15
3
18
23
27
4
16
21
25
5
12
16
22
6
21
23
28
To generate operating funds, the company must sell at least $20 million worth of assets in year 1, $25 million in year 2, and $35 million in year 3. Globex wants to develop a plan for selling these companies during the next 3 years to maximize return.
Formulate a binary programming model for this problem and solve it by using the computer.

To formulate a binary programming model for this problem, we need to define decision variables, objective function, and constraints.

Decision Variables:
Let Xi,j, where i = 1 to 6 and j = 1 to 3, be a binary variable that represents whether company i is sold in year j or not. If Xi,j = 1, it means company i is sold in year j.

Objective Function:
Since we want to maximize the return, the objective function can be defined as the sum of the estimated returns of the sold companies:

Maximize Z = 14*X1,1 + 18*X1,2 + 23*X1,3 + 9*X2,1 + 11*X2,2 + 15*X2,3 + 18*X3,1 + 23*X3,2 + 27*X3,3 + 16*X4,1 + 21*X4,2 + 25*X4,3 + 12*X5,1 + 16*X5,2 + 22*X5,3 + 21*X6,1 + 23*X6,2 + 28*X6,3

Constraints:
1. Each company can be sold only once in one of the three years:

X1,1 + X1,2 + X1,3 = 1
X2,1 + X2,2 + X2,3 = 1
X3,1 + X3,2 + X3,3 = 1
X4,1 + X4,2 + X4,3 = 1
X5,1 + X5,2 + X5,3 = 1
X6,1 + X6,2 + X6,3 = 1

2. The total amount sold in each year should meet the minimum requirements:

14*X1,1 + 9*X2,1 + 18*X3,1 + 16*X4,1 + 12*X5,1 + 21*X6,1 >= 20 (Year 1)
18*X1,2 + 11*X2,2 + 23*X3,2 + 21*X4,2 + 16*X5,2 + 23*X6,2 >= 25 (Year 2)
23*X1,3 + 15*X2,3 + 27*X3,3 + 25*X4,3 + 22*X5,3 + 28*X6,3 >= 35 (Year 3)

3. All decision variables should be binary:

X1,1, X1,2, X1,3, X2,1, X2,2, X2,3, X3,1, X3,2, X3,3, X4,1, X4,2, X4,3, X5,1, X5,2, X5,3, X6,1, X6,2, X6,3 ∈ {0, 1}

Once the binary programming model is formulated, you can use a computer software or solver to solve the model and obtain the optimal solution.