QUESTION $4$

Our company is considering undertaking some projects. We have defined a model with decision variables $x1,x2,x3,x4,$dots for the projects and have put in an optimization model.

$($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 a$)+,$ you enter $"+"($without the quotation marks

obviously$).$

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

You must fill all the blanks for the formula to be fully correct. If your formula is like $x1x2$ but the question reads as $x1x2,$ please enter $x1-$ X$20.$

Questions are graded automatically. If you do not follow the formatting, then your answer will be graded wrong. If your answer is correct, I will be able to manually change your grade for

those questions later, but you will lose $25\%$ of the points. NO EXCEPTIONS, in order to be fair to everyone in the class.$)$

A$.$ The company cannot undertake all of $x1,x2,$ and $x3$ together.

X$1$

$x2$

$x3$

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$)>$ f$)$

Choices for the fourth blank: a$)0$

b$)-1$

c$)1$

d$)2$

B$.$ If the company undertakes $x5,$ it cannot undertake more than two of $x1,x2,x3,$ or $x4.$

$x1$

$72$

$x3$

$x5$

Choices for the first blank: a$)+$ b$)-$ c$)*$ d$)\frac{?}{?}$

Choices for the second blank: a$)+$ b$)-$ c$)*$ d$)\frac{?}{?}$

Choices for the third blank: a$)+$ b$)-$ c$)*$ d$)\frac{?}{?}$

Choices for the fourth blank: a$)$ b$)$ c$)=$ d$)>$ e$)$

Choices for the fifth blank: a$)-1$ b$)0$ c$)0\mathrm{.}5$ d$)1$ e$)2$ f$)3$ g$)4$

Choices for the sixth blank: a$)+$ b$)-$ c$)*$ d$)\frac{?}{?}$

Choices for the seventh blank: a$)0$ b$)0\mathrm{.}5$ c$)1$ d$)2$ e$)3$ f$)4$

Choices for the eighth blank: a$)+$ b$)-$ c$)*$ d$)\frac{?}{?}$

C$.$ If we undertake project $6,$ we need to have at least $2$ million dollars in a checking account. The amount in the checking account is a decision variable L$6.$

L$6$

$2000000$

$x6$

Choices for the first blank: a$)$ b$),)=$

Choices for the second blank: a$)+$ b$)-$ c$)*$ d$)/$

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