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

Max,$3500x_1+5500x_2+10000x_3+3500x_4+8500x_5+2500x_6$

s$.$t$.$

Year $11000x_1+2500x_2+6000x_3+2000x_4+5000x_5+1000x_{6}9000$

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Year $21000x_1+3500x_2+4000x_3+1500x_4+1000x_5+500x_{6}11000$

Year $34000x_1+3500x_2+5000x_3+1800x_4+4000x_5+900x_{6}12000$

warehouse

expansions

expansions

Enter inequalities using less than $(),$ greater than $(>),$ less than $or$ equal $(s),or$ greater than $or$ equal $(z).$

$x_l=0,1$ 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 $ $)?$

$$1$

W$$at Is clle IIIpact

Compared to the optimal NPV from part $($b$),$ the optimal NPV $-$ Select$--$ with the additional constraint.