Linear Programming Model _Excel Solution Module 7 Problem P8-14_P8-28_P9-16_P9-20_Excel_ Answer

Linear Programming Model _Excel Solution Module 7 Problem P8-14_P8-28_P9-16_P9-20_Excel_ Answer

Problem P 8-14

Steve’s Mountain Bicycle Shop is considering three options for its facility next year. Steve can expand his current shop, move to a larger facility,
or make no change. With a good market, the annual payoff would be $76,000 if he expands, $90,000 if he moves, and $40,000 if he does nothing. With
an average market, his payoffs will be $30,000,
$41,000, and $15,000, respectively. With a poor
market, his payoff will be – +17,000, – +28,000, and
$4,000, respectively.
(a) Which option should Steve choose if he uses the
maximax criterion?
(b) Which option should Steve choose if he uses the
maximin criterion?
(c) Which option should Steve choose if he uses the
equally likely criterion?
(d) Which option should Steve choose if he uses
the criterion of realism with a = 0.4?
(e) Which option should Steve choose if he uses
the minimax regret criterion?

Question

Problem P 8-28

Jerry Young is thinking about opening a bicycle shop in his hometown. Jerry loves to take his own bike on 50-mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. Because there will be a five-year lease on the building that Jerry is thinking about using, he wants to make sure that he makes the correct decision. Jerry has done some analysis about the profit-ability of the bicycle shop. If Jerry builds the large bicycle shop, he will earn $60,000 if the market is good, but he will lose $40,000 if the market is bad. The small shop will return a $30,000 profit in a good
market and a $10,000 loss in a bad market. At the
present time, he believes that there is a 59% chance
that the market will be good.
Jerry also has the option of hiring his old mar-
keting professor for $5,000 to conduct a marketing
research study. If the study is conducted, the results
could be either favorable or unfavorable. It is esti-
mated that there is a 0.6 probability that the survey
will be favorable. Furthermore, there is a 0.9 proba-
bility that the market will be good, given a favorable
outcome from the study. However, the marketing
professor has warned Jerry that there is only a prob-
ability of 0.12 of a good market if the marketing
research results are not favorable.
(a) Develop a decision tree for Jerry and help him
decide what he should do.
(b) How much is the marketing professor’s infor-
mation worth? What is the efficiency of this
information?

Problem P 9-16

The wheat harvesting season in the U.S. Midwest is short, and most farmers deliver their truckloads of wheat to a giant central storage bin within a two-
week span. Because of this, wheat-filled trucks waiting to unload and return to the fields have been known to back up for a block at the receiving bin.
The central bin is owned cooperatively, and it is to every farmer’s benefit to make the unloading/storage process as efficient as possible. The cost
of grain deterioration caused by unloading delays
and the cost of truck rental and idle driver time are
significant concerns to the cooperative members.
Although farmers have difficulty quantifying crop
damage, it is easy to assign a waiting and unloading
cost for truck and driver of $18 per hour. The stor-
age bin is open and operated 16 hours per day, seven
days per week during the harvest season and is
capable of unloading 35 trucks per hour, according
to an exponential distribution. Full trucks arrive all
day long (during the hours the bin is open), at a rate
of about 30 per hour, following a Poisson pattern.
To help the cooperative get a handle on the
problem of lost time while trucks are waiting in line
or unloading at the bin, find the
(a) average number of trucks in the unloading
system
(b) average time per truck in the system
(c) utilization rate for the bin area
(d) probability that there are more than three trucks
in the system at any given time
(e) total daily cost to the farmers of having their
trucks tied up in the unloading process
(f) The cooperative, as mentioned, uses the storage
bin only two weeks per year. Farmers estimate
that enlarging the bin would cut unloading costs
by 50% next year. It will cost $9,000 to do so
during the off-season. Would it be worth the
cooperative’s while to enlarge the storage area?

Problem P 9-20

Carlos Gomez is the receiving supervisor for a large grocery store. Trucks arrive to the loading dock at an average rate of four per hour, according to a Pois-
son distribution, for 8 hours each day. The cost of operating a truck is estimated to be $80 per hour. Trucks are met by a three-person crew, which is able
to unload a truck in an average of 12 minutes, according to an exponential distribution. The payroll cost associated with hiring a crew member, includ-
ing benefits, is $22 per hour. Carlos is now considering the installation of new equipment to help the crew, which would decrease the average unload-
ing time from 12 minutes to 9 minutes. The cost of this equipment would be about $500 per day. Is the installation of the new equipment economically
feasible?

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Linear Programming Model Steve’s Mountain Bicycle Shop is considering three options for its facility next year Answer