Reference no: EM132720678

An integer linear programming model is defined using the following sets, parameters, binary decision variables, and objective function. Use this notation to answer the questions below that ask you to translate logic statements into linear constraints.

Sets:
Items I, indexed on i=1, 2... |I|.
Parameters:
ai= 1 if item i is green; 0 otherwise.
Binary Decision Variables:
Xi = 1 if item i is selected; 0 otherwise.
Objective Function:
Maximize the profit of the items selected.

a. Provide a linear constraint to enforce that at least 3 items of any color must be selected.

b. Provide a linear constraint to enforce that at most 2 items of color green can be selected.

c. Provide a linear constraint to enforce that if item 4 is selected then item 1 must not be selected.

d. Provide a linear constraint to enforce that if item 5 is selected, then items 2 and 3 must be selected.

e. Briefly explain in words (that your grandfather would understand) the meaning of this constraint: x1 + x2 ≤ 1.