$(20$ points$)$ Nancy is traveling during the Memorial Day holiday and is renting out her apartment in Manhattan, NY$,$ from May $26$th to May $30$th $($a total of five days$).$ She has received many bids on Airbnb, each with the following form: the day the rental starts $($a rental day starts at $3$ p$.$m$.),$ the day the rental ends $($checkout time is noon$),$ and the money $($in dollars$)$

the renter will pay for this duration.

$$ Bid $1$: $$400$ for check$-$in: May $26,$ check$-$out: May $27$

$$ Bid $2$: $$800$ for check$-$in: May $26,$ check$-$out: May $28$

$$ Bid $3$: $$1300$ for check$-$in: May $26,$ check$-$out: May $29$

$$ Bid $4$: $$1250$ for check$-$in: May $27,$ check$-$out: May $30$

$$ Bid $5$: $$450$ for check$-$in: May $28,$ check$-$out: May $29$

$$ Bid $6$: $$350$ for check$-$in: May $29,$ check$-$out: May $30$

$$ No bids are made for check$-$in: May $27,$ check$-$out: May $28$

In order to determine which bids Nancy should accept to maximize her annual rental income:

$($a$)$ Develop a shortest network model to illustrate the given problem $(10$pt$)$

$($b$)$ Find the optimal bids using Dijkstra$$s algorithm. $(10$pt$)$