X1, X2, and X3 are three Binary decision variables corresponding to whether or not to overtake projects 1, 2, and 3 in a maximization problem. In the following, I provide 4 different constraints and the corresponding equation for them and ask you to fill the blanks.

(Note that:

I want your models to be linear.

Also, the question is going to be graded automatically. Therefore, I give you options for the blanks and your solution must be chosen from the options. Make sure that you type the exact choices (not the choice number) per blank. No spaces, quotation marks, or anything extra. For instance, if it is choice 1) +, you enter "+" (without the quotation marks obviously).

Consider each part independently. Also, each part is graded separately.)

A. In order to avoid monopoly, the regulator does not allow us to undertake all three projects together. X1 X2 X3

Choices for the first blank: a) + b) - c) * d) / Choices for the second blank: a) + b) - c) * d) / Choices for the third blank: a) >= b) <= c) = d) < e) > Choices for the fourth blank: a) 0 b) -1 c) 1 d) 2 e) 3

B. Projects 1 and 2 must either be undertaken simultaneously, or none of them can be undertaken. (In other words, it is impossible to undertake only one of them.) X1 X2

Choices for the first blank: 1) + 2) - 3) * 4) / Choices for the second blank: 1) >= 2) <= 3) = 4) < 5) > 6) Choices for the third blank: 1) 0 2) -1 3) 1 4) 2

C. We cannot abandon all the projects. In other words, we must undertake some of them. ("Some" means "at least one and possibly all.")

X1 X2 X_3

Choices for the first blank: 1) + 2) - 3) * 4) / Choices for the second blank: 1) + 2) - 3) * 4) / Choices for the third blank: 1) >= 2) <= 3) = 4) < 5) > Choices for the fourth blank: 1) 0 2) -1 3) 1 4) 2 5) 3

D. If we want to undertake project 3, we must put a minimum of $10,000 in a certain reserved account. The reserved amount is kept in the cell "F1". *F1 *X3

Choices for the first blank: 1) 1 2) 10,000 3) 1,000,000,000 (a very large number) Choices for the second blank: 1) <= 2) = 3) >= Choices for the third blank: 1) 1 2) 10,000 3) 1,000,000,000 (a very large number)