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skishop

# skishop - Tom's Ski Shop Tom owns a ski shop at the foot of...

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Sheet1 Page 1 Tom's Ski Shop ----- --- ---- Tom owns a ski shop at the foot of Mt. Big Toe. He both sells and rents skis. Tom's customers can either buy skis for X dollars, or rent them for a weekend for Y dollars. If a customer skis for T weekends before he tires of skiing and stops, and if the customer rents for the first K weekends and then buys on the K+1'st week- end, with K+1 <= T, then the customer pays K*Y + X dollars to have skis for T weekends. If X < T*Y, the customer would find it least expensive to have bought skis on his very first weekend (K = 0), but if X > T*Y, the customer would find it least expensive to always rent (K >= T). A customer does not know his T in advance of actually getting tired of skiing, so these last facts are not very useful. Tom has studied this situation statistically and devised `optimal' advice for his customers. By observation, Tom knows the probability P[T] that an arbitrary customer will tire of skiing after exactly T weekends. Using this Tom finds the number K such that if every customer

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skishop - Tom's Ski Shop Tom owns a ski shop at the foot of...

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