Comedy Pasture
A horse and two llamas are discussing the key areas of their domain on a lazy summer
afternoon. The llamas favor the pond and shade and like to browse the fruit trees and
oaks on the property, making their way to the barn only when their owner favors them
with some oats. The horse prefers to graze the grass and hay for food and drink from the
pond but will race up to the barn when the owner is handing out oats up there. Between
the three of them, they have stepped off the distances between many of these key points
several times and believe that they have developed an accurate map, shown below. As
incredible as it may seem, neither the horse nor the llamas have had any training in
management science, which is where you come in.
During the harvest, the horse and llamas are herded up to the orchard where they are
loaded down with fresh-picked fruit. Some of the fruit is taken to the pond to feed the
catfish and the remainder is crated up underneath the shade trees. What is the shortest
route to those locations; provide distance and the path?
The ________ is the percentage of variation in the dependent variable that results from
the independent variable.
Consider the following network.
Identify the critical path.
Given the following linear programming problem:
maximize Z = $100x1 + 80x2
subject to x1 + 2x2 ≤ 40
3x1 + x2 ≤ 60
x1, x2 ≥ 0
Using the simplex method, what is the value for S2 in the optimal tableau?
Napoleon is contemplating four institutions of higher learning as options for a Masters
in Business Administration. Each university has strong and weak points and the demand
for MBA graduates is uncertain. The availability of jobs, student loans, and financial
support will have a significant impact on Napoleon’s ultimate decision. Vanderbilt and
Seattle University have comparatively high tuition, which would necessitate Napoleon
take out student loans resulting in possibly substantial student loan debt. In a tight
market, degrees with that cachet might spell the difference between a hefty paycheck
and a piddling unemployment check. Northeastern State University and Texas Tech
University hold the advantage of comparatively low tuition but a more regional appeal
in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist
with the decision. Together they forecast three possible scenarios for the job market and
institutional success and predict annual cash flows associated with an MBA from each
institution. All cash flows in the table are in thousands of dollars.
Napoleon’s Uncle Rico believes that the scenarios are not necessarily equally likely, and
suggests that the likelihood of occurrence of Scenario 2 is 0.4 and the likelihood of
occurrence of Scenarios 1 and 3 are both 3. What two criteria are most appropriate and
what is the resulting decision?
A large book publisher has five manuscripts that must be edited as soon as possible.
Five editors are available for doing the work, however their working times on the
various manuscripts will differ based on their backgrounds and interests. The publisher
wants to use an assignment method to determine who does what manuscript. Estimates
of editing times (in hours) for each manuscript by each editor is:
If the optimal assignments include manuscript 1 to editor B, manuscript 2 to editor E,
and manuscript 3 to editor C with a total editing time of 47 minutes, what manuscripts
are assigned to editors D and A?
Use the following table to answer the question(s) below.
If the probabilities of s1, s2, and s3 are 0.2, 0.4, and 0.4, respectively, then what decision
should be made under expected value?
Consider the following transportation problem:
How many supply-side constraints are there? Write the supply-side constraints.
A study of a company’s practice regarding the payment of invoices revealed that on the
average an invoice was paid 20 days after it was received. The standard deviation
equaled 5 days. Assuming that the distribution is normal, what percent of the invoices is
paid within 15 days of receipt?
Consider the following linear program, which maximizes profit for two
products–regular (R) and super (S):
MAX 50R + 75S
s.t.
1.2 R + 1.6 S ≤ 600 assembly (hours)
0.8 R + 0.5 S ≤ 300 paint (hours)
.16 R + 0.4 S ≤ 100 inspection (hours)
Sensitivity Report:
The profit on the super product could increase by ________ without affecting the
product mix.
An increase in output typically results in an increase in the ________ cost.
A store has determined that the weekly sales of a product is related to the number of
customers who visit the store and the square feet of shelf space, x, according to the
following equation: -20x2 – 10C2 + 40Cx + 120x – 200C + C represents the hundreds of
customers who visit their store. If a store averages 200 customers per week, how many
square feet of shelf space is required to maximize sales?
Billy Hill’s Still
William J Hill runs a small batch artisnal bourbon distillery at a secluded location in the
hills of Kentucky. He makes two products, known among his customers as Rotgut and
White Lightning. The recipes for the two have been passed down in the Hill family for
generations and are Rotgut: 1 bushel of corn, 3 pounds of sugar, 2 hours of cooking
time. For the premium blend, White Lightning, he needs 2 bushels of corn, 2 pounds of
sugar, and 3 hours of cooking time. Both recipes make enough to fill two jugs, which
sell for $8 apiece for Rotgut and $12 apiece for White Lightning.
A quick inventory one crisp autumn morning reveals that William has on hand 40
bushels of corn, 70 pounds of sugar, and 50 jugs. He would like to brew up a few
artisnal batches, but has recently received a tip that certain agencies have taken an
interest in his talents and may be paying him a visit in three days, hence he plans to
restrict any brewing activity to 72 hours at most, before he retreats to his home away
from home, Lubbock.
William cleans his equipment, lights a fire, and ponders the objectives. Obviously the
first priority is restricting himself to 72 hours of work any more than that and he runs
the risk of an extended holiday. His second priority to make enough to acquire materials
for the next production run and fund his daughter’s college tuition – he believes that
$500 would make this production run worth his while. His third and fourth priorities are
not to have too much perishable inventory, so he wants to make sure he doesn’t have too
many bushels of corn on hand (third priority) nor does he want too many pounds of
sugar on hand (fourth priority).What is the sugar constraint?
3R + 2W + d4
In a ________ problem, artificial variables are assigned a very high cost.
A management science technique that does not assume that all parameters are known
with certainty is a(n) ________ technique.
The number of cars arriving at Joe Kelly’s oil change and tune-up place during the last
200 hours of operation is observed to be the following:
Based on the above frequencies, use two-digit random numbers, start with random
number 00, and determine the random number ranges for the data set given above.
Given an EOQ model with shortages in which annual demand is 4200 units, Co = $160,
Cc = $7 per unit per year and CS = $25, what is the optimal order quantity?