Select the correct answers below.$$Optimal Solution:

x$1-$ Select your answer $-01$Item $31$ x$2-$ Select your answer $-01$Item $32$ x$3-$ Select your answer $-01$Item $33$ x$4-$ Select your answer $-01$Item $34$ x$5-$ Select your answer $-01$Item $35$ x$6-$ Select your answer $-01$Item $36$

$$Net Present Value: $ $($b$)$Assume that only one of the warehouse expansion projects can be implemented. Modify your model of part $($a$).$ Which of the following constraint must be added to the model?

$($i$)$x$1=$ x$2($ii$)$x$1+$ x$21($iii$)$x$1+$ x$21($iv$)$None of the above.

$-$ Select your answer $-$Option $($i$)$Option $($ii$)$Option $($iii$)$Option $($iv$)$Item $38($c$)$Suppose that, if test marketing of the new product is carried out, the advertising campaign also must be conducted. Modify your formulation of part $($b$)$ to reflect this new situation. Which of the following constraint must be added to the model in part $($b$)?$

$($i$)$x$3$ x$4($ii$)$x$4$ x$3($iii$)$x$3+$ x$41($iv$)$x$3+$ x$41$

$-$ Select your answer $-$Option $($i$)$Option $($ii$)$Option $($iii$)$Option $($iv$)$Item $39$