Question $3(15$ points$)$

Kim electronics sells personal computers through catalogs. Catalogs are printed once every

year. Each printing run incurs a variable production cost of $$10$ per catalog. Annual

demand for catalogs is estimated to follow the distribution as below:

On average, each customer ordering a catalog generates a profit

of $$40$ from sales $($this profit doesn't consider a variable

production cost of $$10$ per catalog$).$ Assume that Kim

electronics wants only one printing run in each one$-$year cycle

and outdated catalogs will be useless.

a$)(5$ pts$)$ What is the optimal service level for Kim electronics to maximize its profit?

b$)(5$ pts$)$ How many catalogs should be prepared in each run?

c$)(5$ pts$)$ If the variable production cost increases to $$20$ per catalog, how many

catalogs should be prepared in each run?