PA $13-9($ Algo $)$ ?CPG Bagels starts the day with a large production...

CPG Bagels starts the day with a large production run of bagels. Throughout the morning, additional bagels are produced as needed.

The last bake is completed at $3$ ?p $.$ m $.$ ?and the store closes at $8$ ?p $.$ m $.$ ?It costs approximately $ $0\mathrm{.}25$ ?in materials and labor to make a bagel.

The price of a fresh bagel is $ $0\mathrm{.}65.$ ?Bagels not sold by the end of the previous day are sold the next day as "day old" bagels in bags of

six for $ $0\mathrm{.}99$ a bag. About two $-$ thirds of the day $-$ old bagels are sold; the remainder are just thrown away. There are many bagel flavors,

but for simplicity, concentrate just on the plain bagels. The store manager predicts that demand for plain bagels from $3$ ?p $.$ m $.$ ?until

closing is normally distributed with a mean of $59$ ?and a standard deviation of $30.$ ?Use Table $13\mathrm{.}4.$

Note: If a part of the question specifies whether to use Table $13\mathrm{.}4,$ ?or to use Excel, then credit for a correct answer will depend on

using the specified method.

a $.$ ?How many bagels should the store have at $3$ ?p $.$ m $.$ ?to maximize the store's expected profit $($ from sales between $3$ ?p $.$ m $.$ ?until closing $)?$

$($ Hint: Assume day $-$ old bagels are sold for $ $0\mathrm{.}996=$ $ $0\mathrm{.}165$ ?each, that is $,$ ?don't worry about the fact that day $-$ old bagels are sold in

bags of six. $)$ ?Use Table $13\mathrm{.}4$ ?and round $-$ up rule.

Order quantity

b $.$ ?Suppose the store manager has $97$ ?bagels at $3$ ?p $.$ m $.$ ?How many bagels should the store manager expect to have at the end of the

day? Use Table $13\mathrm{.}4$ ?and round $-$ up rule.

Note: Round your answer to a whole number.

Expected inventory

c $.$ ?Suppose the manager would like to have a $0\mathrm{.}96$ ?in $-$ stock probability on demand that occurs after $3$ ?pm $.$ ?How many bagels should

the store have at $3$ ?p $.$ m $.$ ?to ensure that level of service? Use Table $13\mathrm{.}4$ ?and round $-$ up rule.