Harney Accommodations Industries $($HAI$)$ operates the only two hotels in the town of Burns. The

Historic Central Hotel $($CH$)$ is a three$-$star, prohibition$-$themed hotel right downtown; one review even

says it feels like the Shining without the hauntings. The CH charges customers $$160$ per night with

constant marginal cost of renting each room of $$30$ per night $($from cleaning and laundry.$)$ Silver Spur

Motel is a one$-$star motel offering a clean room but no frills. Silver Spur Motel charges $$60$ per night

with constant marginal cost of renting each room of $$20$ per night $($from cleaning and laundry.$)$

Both hotels operate as independent profit centers within HAI. Each hotel has its own management and

makes its own decisions about operations and marketing. For both hotels, the annual bonuses earned

by management depend only on the profits earned by that hotel, not on the overall profit of HAI. This

means that each hotel's management makes decisions that maximize the profit of only its own hotel.

The CH Manager, Ms$.$ Silvies, relies on Instagram advertising to attract her upper$-$middle class clientele.

Ms$.$ Silvies is currently weighing whether to do a large or small Instagram campaign in July. She estimates

that her July average nightly occupancy will be $6$ rooms if she does a small campaign, but that this

number will be $10$ if she instead does a large campaign. While this bump in occupancy is attractive to

Ms$.$ Silvies, Instagram advertising is expensive. The cost of a small campaign is $$5,000,$ but the cost of a

large campaign is $$15,000.$

The Silver Spur Motel Manager, Mr$.$ Hines, relies instead on billboard advertising to draw weary road

warriors off Highway $20$ to his motel. Mr$.$ Hines is currently weighing whether to do a large or small

billboard campaign in July. He estimates that his July average nightly occupancy will be $25$ rooms if he

does a small campaign, but that this number will be $45$ if he instead does a large campaign. While this

bump in occupancy is attractive to Mr$.$ Hines, billboard advertising is expensive. The cost of a small

campaign is $$10,000,$ but the cost of a large campaign is $$20,000.$

Interestingly, Silver Spur Motel billboards are occasionally noticed by well$-$to$-$do auto travelers, who then

stop in Burns but choose to stay at the CH$.$ Because of this effect, if Mr$.$ Hines runs a large billboard

campaign, then the July average nightly occupancy at the CH is higher by $20\%($compared to what it

otherwise would be$).$ Similarly, Instagram ads for the Historical CH at Burns are occasionally noticed by

bargain$-$conscious travelers, who then visit the town but choose to stay at Silver Spur Motel. Because of

this effect, if Ms$.$ Silvies runs a large Instagram campaign, then the July average nightly occupancy at

Silver Spur Motel is higher by $15\%($compared to what it otherwise would be$).$