The Cruise

Their cruise would port out of New Orleans and promised seven days with a panoply of excursions in Jamaica, Cozumel, and Grand Cayman. A list of excursions at each site and key features of each appear in the table. The excursions were all day affairs, so it was possible to engage in only one per port. The cruise ship sailed at night and docked at each of these three ports at the crack of dawn. By dinner time, the ship was on its way to the next port and next set of excursions. The couple was energetic and active for a pair of $52-$year$-$olds, and while enjoying an upper middle class lifestyle, they didn't want to spend money on excursions that might be better spent on tacky souvenirs. The couple therefore budgeted $$250$ for the excursions $-$ the prices shown are per couple, so for example, the $$60$ will pay for both of them to fill up on jerk chicken and mannish water.

For each of the duplicate excursions $($e$.$g$.,$ snorkeling is offered in all three ports$),$ the couple researched the quality of the activity and ranked the excursion among the available alternatives, with higher numbers indicating better quality. Thus, snorkeling in Jamaica is better than in Cozumel, and snorkeling in Cozumel is better than in Grand Cayman. For the unique experiences, i$.$e$.,$ the turtle farm, the default rating was the a $3.$

Site Rating Activity Cost

Jamaica $3$ snorkeling $$100$

Jamaica $1$ party island $$95$

Jamaica $2$ horseback ride $$120$

Jamaica $3$ local cuisine $$60$

Cozumel $2$ snorkeling $$110$

Cozumel $3$ party island $$55$

Cozumel $1$ horseback ride $$70$

Cozumel $2$ local cuisine $$90$

Cozumel $3$ tequila tasting $$130$

Grand Cayman $1$ snorkeling $$90$

Grand Cayman $2$ party island $$60$

Grand Cayman $3$ horseback ride $$110$

Grand Cayman $1$ local cuisine $$130$

Grand Cayman $3$ turtle farm $$95$

$($Note $-$ data used in this test question should not be construed as vacation advice.$)$

In all the excitement of waving to the longshoremen as the ship leaves the Port of New Orleans, the management scientist drops his wallet in the Mississippi River. Rather than maximize enjoyment for the three excursions, he must now adjust his model to select three inexpensive options. Which combinations of objective function and constraints are best if the scheme of location $($J$,$ C$,$ or G$)$ and excursion $($S$,$ P$,$ H$,$ L$,$ Te or Tu$)$ is used to represent the decision variables?

Group of answer choices

Min Z $=100$JS $+95$JP $+120$JH $+60$JL $+110$CS $+55$CP $+70$CH $+90$CL $+130$CTe $+90$GS $+60$GP $+110$GH $+130$GL $+95$GTu

subject to:

JS $+$ JP $+$ JH $+$ JL $=1$

CS $+$ CP $+$ CH $+$ CL $+$ CTe $=1$

GS $+$ GP $+$ GH $+$ GL $+$ GTu $=1$

Min Z $=100$JS $+95$JP $+120$JH $+60$JL $+110$CS $+55$CP $+70$CH $+90$CL $+130$CTe $+90$GS $+60$GP $+110$GH $+130$GL $+95$GTu

subject to:

JS $+$ JP $+$ JH $+$ JL $<=1$

CS $+$ CP $+$ CH $+$ CL $+$ CTe $<=1$

GS $+$ GP $+$ GH $+$ GL $+$ GTu $<=1$

Min Z $=100$JS $+95$JP $+120$JH $+60$JL $+110$CS $+55$CP $+70$CH $+90$CL $+130$CTe $+90$GS $+60$GP $+110$GH $+130$GL $+95$GTu

JS $+$ CS $+$ GS $<=1$

JP $+$ CP $+$ GP $<=1$

JH $+$ CH $+$ GH $<=1$

JL $+$ CL $+$ GL $<=1$

Min Z $=100$JS $+95$JP $+120$JH $+60$JL $+110$CS $+55$CP $+70$CH $+90$CL $+130$CTe $+90$GS $+60$GP $+110$GH $+130$GL $+95$GTu

JS $+$ JP $+$ JH $+$ JL $+$ CS $+$ CP $+$ CH $+$ CL $+$ CTe $+$ GS $+$ GP $+$ GH $+$ GL $+$ GTu $=3$