warehouse expansion alternatives can be chosen

$($a$)$ Develop an integer programming model for maximizing the net present value $($in $ $).($Let $x_i=1$ if investment alternative $i$ is selected, $0$ otherwise, for $i=1,2,3,4,5,6.)$

Max

s$.$t$.$

Year $1$

Year $2$

Year $3$

warehouse

expansions

$x_i=0,1$ for $i=1,2,3,4,5,6$

According to this model, what is the maximum net present value $($in $ $)?$

$($b$)$ Suppose that if the Advertising campaign is chosen, then the Test market new product alternative must be chosen. Modify your model from part $($a$)$ to take this into account.

In addition to the constraints from part $($a$),$ what additional constraint should be added to the integer programming model?

According to this model, what is the maximum net present value $($in $ $)?$

$$[,]$

$($c$)$ Suppose the Extensive warehouse expansion must be chosen. Modify your formulation from part $($b$)$ to reflect this new situation.

In addition to the constraints from part $($a$)$ and part $($b$),$ what additional constraint should be added to the integer programming model?

According to this model, what is the maximum net present value $($in $ $)?$

$$|$

What is the impact of this constraint on the optimal NPV in comparison to the optimal NPV from part $($b$)?$

Compared to the optimal NPV from part $($b$),$ the optimal NPV $[$

vith the additional constraint.