Capacity$-$based RM$)$ HK$4$ is a television station that has $25$ thirty$-$second advertising

slots during each evening. It is early January and the station is selling advertising for

Sunday, March $24.$ They could sell all of the slots right now for $$4,000$ each, but,

because on this particular Sunday the station is televising the Oscar ceremonies, there

will be an opportunity to sell slots during the week right before March $24$ for a price of

$$10,000.$ For now, assume that a slot not sold in advance and not sold during the last

week is worthless to HK$4.$ To help make this decision, the salesforce has created the

following probability distribution for last$-$minute sales:

$29$

Number of slots,

x

Pr$($Exactly x

slots are sold$)$

$80\mathrm{.}00$

$90\mathrm{.}05$

$100\mathrm{.}10$

$110\mathrm{.}15$

$120\mathrm{.}20$

$130\mathrm{.}10$

$140\mathrm{.}10$

$150\mathrm{.}10$

$160\mathrm{.}10$

$170\mathrm{.}05$

$180\mathrm{.}05$

$190\mathrm{.}00$

Cumulative Prob

$0\mathrm{.}00$

$0\mathrm{.}05$

$0\mathrm{.}15$

$0\mathrm{.}30$

$0\mathrm{.}50$

$0\mathrm{.}60$

$0\mathrm{.}70$

$0\mathrm{.}80$

$0\mathrm{.}90$

$0\mathrm{.}95$

$1\mathrm{.}00$

$1\mathrm{.}00$

a$.$ How many slots should HK$4$ sell in advance?

Supply:

Demand:

Cu $($undersupply$)$:

Co $($oversupply$)$:

Capacity$-$based RM: Protection