CPG Bagels starts the day with a large production run of bagels. Throughout the morning, additional bagels are produced
Posted: Tue Apr 26, 2022 12:47 pm
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.)
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.)