# Case studies 3 and 4

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Ch. 6-Case Problem-Go Bananas!
Great Grasslands Grains, Inc. (GGG) manufactures and sells a wide variety of breakfast cereals. GGG’s
product development lab recently created a new cereal that consists of rice flakes and banana-flavored
marshmallows. The company’s marketing research department has tested the new cereal extensively
and has found that consumers are enthusiastic about the cereal when 16-ounce boxes contain at least
1.6 ounces and no more than 2.4 ounces of the banana-flavored marshmallows.
As GGG prepares to begin producing and selling 16-ounce boxes of the new cereal, which it has named
Go Bananas management is concerned about the amount of banana-flavored marshmallows. It wants to
be careful not to include less than 1.6 ounces or more than 2.4 ounces of banana-flavored
marshmallows in each 16-ounce box of Go Bananas. Tina Finkel, VP of Production for GGG, has
suggested that the company measure the weight of banana-flavored marshmallows in a random sample
of 25 boxes of Go Bananas on a weekly basis. Each week, GGG can count the number of boxes out of the
25 boxes in the sample that contain less than 1.6 ounces or more than 2.4 ounces of banana-flavored
marshmallows; if the number of boxes that fail to meet the standard weight of banana-flavored
marshmallows is too high, production will be shut down and inspected.
Ms. Finkel and her staff have designed the production process so that only 8% of all 16-ounce boxes of
Go Bananas fail to meet the standard weight of banana-flavored marsh-mallows (the probability of
failing to meet the standard is 0.08). After much debate, GGG management has decided to shut down
production of Go Bananas if at least five boxes in a weekly sample fail to meet the standard weight of
banana-flavored marshmallows.
Prepare a managerial report that addresses the following issues.
1. Calculate the probability that a weekly sample will result in a shutdown of production if the
production process is working properly. Comment on GGG management’s policy for deciding
when to shut down production of Go Bananas!
2. GGG management wants to shut down production of Go Bananas no more than 1% of the time
when the production process is working properly. Suggest the appropriate number of boxes in
the weekly sample that must fail to meet the standard weight of banana-flavored marshmallows
in order for production to be shut down if this goal is to be achieved.
3. Ms. Finkel has suggested that if given sufficient resources, she could redesign the production
process to reduce the percentage of 16-ounce boxes of Go Bananas that fail to meet the
standard weight of banana-flavored marshmallows when the process is working properly. To
what level must Ms. Finkel reduce the percentage of 16-ounce boxes of Go Bananas that fail to
meet the standard weight of banana-flavored marshmallows when the process is working
properly in order for her to reduce the probability at least five of the sampled boxes fail to meet
the standard to .01 or less?
Ch. 7-Case Problem-Specialty Toys
Specialty Toys, Inc., sells a variety of new and innovative children’s toys. Management learned that the
preholiday season is the best time to introduce a new toy, because many families use this time to look
for new ideas for December holiday gifts. When Specialty discovers a new toy with good market
potential, it chooses an October market entry date. In order to get toys in its stores by October,
Specialty places one-time orders with its manufacturers in June or July of each year. Demand for
children’s toys can be highly volatile. If a new toy catches on, a sense of shortage in the market place
often increases the demand to high levels and large profits can be realized. However, new toys can also
flop, leaving Specialty stuck with high levels of inventory that must be sold at reduced prices. The most
important question the company faces is deciding how many units of a new toy should be purchased to
meet anticipated sales demand. If too few are purchased, sales will be lost; if too many are purchased,
profits will be reduced because of low prices realized in clearance sales. For the coming season,
Specialty plans to introduce a new product called Weather Teddy. This variation of a talking teddy bear
is made by a company in Taiwan. When a child presses Teddy’s hand, the bear begins to talk. A built-in
barometer selects one of five responses that predict the weather conditions. The responses range from
“It looks to be a very nice day! Have fun.” to “I think it may rain today. Don’t forget your umbrella.” Tests
with the product show that, even though it is not a perfect weather predictor, its predictions are
surprisingly good. Several of Specialty’s managers claimed Teddy gave predictions of the weather that
were as good as many local television weather forecasters. As usual, Specialty faces the decision of how
many Weather Teddy units to order for the coming holiday season. Members of the management team
suggested order quantities of 15,000, 18,000, 24,000, or 28,000 units. The wide range of order
quantities suggested indicate considerable disagreement concerning the market potential. The product
management team asks you for an analysis of the stock-out probabilities for various order quantities, an
estimate of the profit potential, and to help make an order quantity recommendation. Specialty expects
to sell Weather Teddy for \$24 based on a cost of \$16 per unit. If inventory remains after the holiday
season, Specialty will sell all surplus inventory for \$5 per unit. After reviewing the sales history of similar
products, Specialty’s senior sales forecaster predicted an expected demand of 20,000 units (mean) with
a 0.95 probability that demand would be between 10,000 units and 30,000 units.
Prepare a managerial report that addresses the following issues and recommends an order quantity for
the Weather Teddy product.
1. Use the sales forecaster’s prediction to describe a normal probability distribution that can be
used to approximate the demand distribution. Show the mean and standard deviation of the
distribution.
2. Compute the probability of a stock-out for the order quantities suggested by members of the
management team.
3. Compute the projected profit for the order quantities suggested by the management team
under three scenarios: worst case in which sales = 10 000 units, most likely case in which sales =
20000 units, and best case in which sales = 30 000 units.
4. One of Specialty’s managers felt that the profit potential was so great that the order quantity
should have a 70% chance of meeting demand and only a 30% chance of any stock-outs. What
quantity would be ordered under this policy, and what is the projected profit under the three
sales scenarios?