Operations Management: Homework Assignment $4$

Due on $11$:$59$pm$,$ April $29{?}^{th},2024$

Q$1.$ Betty's Bagel Bakery, inc.

Betty bakes and sells bagels $7$ days a week all year around. Betty has to plan and manage

inventories of paper take$-$out bags with her logo printed on them to satisfy customer demands.

Daily demand for take$-$out bags is normally distributed with a mean of $90$ bags and a standard

deviation of $30$ bags. Betty's printer charges her $$10$ per order for print setup independent of

order size. Bags are printed at $5$ cents $($ $$0\mathrm{.}05)$ each bag. It takes $4$ days for an order to be printed

and delivered. Betty has a storage room big enough to hold all reasonable quantities of bags;

its operating expenses may be regarded as fixed. The only holding cost is the opportunity cost

of capital, which is estimated to be $25\%$ per year. Assume $360$ days per year.

a$.$ What is the optimal order quantity per order for Betty?

b$.$ How many times per year does Betty need to order?

c$.$ How many days will elapse between two consecutive orders?