The University of Miami bookstore stocks textbooks in preparation for sales each semester. It normally relies on departmental forecasts and preregistration records to determine how many copies of a text are needed. Preregistration shows $95$ operations management students$$ enrolled, but bookstore manager Vaidy Jayaraman has second$$ thoughts, based on his intuition and some historical evidence. Vaidy believes that the distribution of sales may range from $75$ to $95$units$,$ according to the following probability$$ model:

$$

Demand

$75$

$80$

$85$

$90$

$95$

Probability

$0\mathrm{.}05$

$0\mathrm{.}20$

$0\mathrm{.}25$

$0\mathrm{.}20$

$0\mathrm{.}30$

This textbook costs the bookstore $ $70$ and sells for $ $95.$ Any unsold copies can be returned to the$$ publisher, less a restocking fee and$$ shipping, for a net refund of $ $30.$

Part $2$

$$a$)$ Based on the given$$ information, Vaidy's conditional profits table for the bookstore$$ is:

Demand

$75$

$80$

$85$

$90$

$95$

Stock

pequals$0\mathrm{.}05$

pequals$0\mathrm{.}20$

pequals$0\mathrm{.}25$

pequals$0\mathrm{.}20$

pequals$0\mathrm{.}30$

$75$

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