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

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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 $0.20 in materials and labor to make a
bagel. The price of a fresh bagel is $0.60. Bagels not sold by the
end of the day are sold the next day as “day old” bagels in bags of
six, for $0.99 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 47 and a
standard deviation of 21.
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 $0.99/6 = $0.165 each; that is, don’t worry about the fact
that day-old bagels are sold in bags of six.) (Round
your answer to the nearest whole number.)
b. Suppose that the store manager is concerned that stockouts
might cause a loss of future business. To explore this idea, the
store manager feels that it is appropriate to assign a stockout
cost of $5 per bagel that is demanded but not filled. (Customers
frequently purchase more than one bagel at a time. This cost is per
bagel demanded that is not satisfied rather than per customer that
does not receive a complete order.) Given the additional stockout
cost, how many bagels should the store have at 3 p.m. to
maximize the store’s expected profit? (Round your
answer to the nearest whole number.)
c. Suppose the store manager has 107 bagels at 3 p.m. How many
bagels should the store manager expect to have at the end of the
day? (Round your answer to the nearest whole
number.)