The model was entered into an Excel spreadsheet and the table below shows part of the
sensitivity report. Calculate the expected per unit profit for the three services.
Formulate the goal programming model.
3R + 2W + d4
The dual value of a resource in a nonlinear programming model is given by the
________.
A ________ solution is not guaranteed by rounding down non-integer solution values.
A ________ integer model allows for the possibility that some decision variables are
not integers.
Given the nonlinear programming model Max Z = 5×1 – 2x2
2
Subject to: x1 + x2 = 6
What is the Lagrangian function?
5x1 – 2x2
The drying rate in an industrial process is dependent on many factors and varies
according to the following distribution.
Compute the mean drying time.
If total contribution of is expressed as C = 60x1 – 5x1
2 + 80x2 – 4x2
2 and x1 = 2x2, then
the Lagrangian function is 60x1 – 5x1
2 + 80x2 – 4x2
2 ________.
The only car dealership in a community stocks cars from two manufacturers, Fret and
Cessy. The following transition matrix shows the probabilities of a customer purchasing
each brand of car in the next year given that he or she purchased that car in the current
year.
Determine the steady state probabilities for Fret and Cessy.
Cold & Calculating
The cold, calculating father did exactly that when examining the 27 year old failure to
launch man child that had turned his walk in closet into a bedroom. As he saw it, there
were five alternatives; each had its advantages and disadvantages, and under different
circumstances, each had a different financial incentive. He laid it all out neatly in a
table, but as not to arouse suspicion, he left the table’s labels very generic, so the
alternatives were simply labeled A through E while the different circumstances were
simply numbered one through three. He flicked the gray ash off of his favorite purple
smoking jacket and pondered the best course of action under each possible future. It
was good to be devious, he decided.
He set the analysis aside for a few days and had forgotten about it completely until one
night when his frequent dining companion Leonid Hurwicz visited his house and retired
to the drawing room for an apertif. “What you must do, my friend,” Hurwicz began, “is
to declare your coefficient of optimism, which can be tricky.” After forty-five minutes
of intense concentration, the cold, calculating father decided that his coefficient of
optimism was 0.5. “Wait a minute Hurwicz, that figure sounds as if I’m afraid of
making a decision,” the father intoned. “It seems that depending on how optimistic I
am, the optimal choice changes between alternative B and alternative D. Furthermore,
another transition point exists between alternatives C and D. What is this devilry,
Hurwicz?”
Help Leonid Hurwicz identify the range of coefficients of optimism that render
alternatives, B, C, and D superior to all others.
Awards committees need to be formed to review potential award recipients. In the past,
three people have been assigned to review each applicant. The only stipulation is that a
reviewer cannot be assigned to an applicant if the applicant is a co-worker. The matrix
below shows 9 reviewers, 3 candidates, and a matrix. If an entry in the matrix contains
an “X”, then that specific reviewer is ineligible to review an applicant’s material. For
example, reviewer 1 cannot review materials submitted by candidate B. It is possible
that some reviewers may not receive an assignment.
Applicant
Formulate this as an assignment problem in which two reviewers are assigned to review
each applicant’s material.
Jim is considering pursuing an MS in Information Systems degree. He has applied to
two different universities. The acceptance rate for applicants with similar qualifications
is 20% for University X and 45% for University Y.
What is the probability that Jim will not be accepted at either university?
Given the following linear programming problem:
maximize 4x1 + 3x2
subject to 4x1 + 3x2 ≤23
5x1 – x2 ≤ 5
x1, x2 ≥ 0
What is the value of x2 in the final tableau?
The injection molding department of Alver Inc. uses an average of 40 pounds of a
special powder per day. The plant operates 250 days per year. The daily usage of the
powder is normally distributed with a standard deviation of 5 pounds per day. The lead
time to obtain the powder from a supplier is 9 days. The annual holding cost is $2 per
unit and the cost of ordering the powder is $50.
Determine the reorder point for a service level of 97%.
Given the following transportation tableauwhere the numbers in each cell represent
transportation costs from the specific source to the specific destinationwith supply
figures corresponding to each source and demand figures corresponding to each
destination:
According to the minimum cell cost method, the initial solution would have a total
transportation cost of ________.
________ variables are added to constraints and represent unused resources.
It was a house with seven cats, four female and three male, and the litterbox was busier
than O’Hare Airport during the week of Thanksgiving. The beleaguered husband’s home
office was right around the corner from the laundry room, where the litterbox was kept,
and heard three separate instances of use. What is the likelihood that none of the
instances were the work of the male cats?
Lush Lawns, Inc. provides a lawn fertilizer and weed control service. They are adding a
special aeration treatment as a low-cost extra service option, which it hopes will help
attract new customers. Management is planning to promote this new service in two
media: radio and direct-mail advertising. A budget of $2000 is to be used on this
promotional campaign over the next quarter. Based on past experience in promoting its
other services, Lush Lawns has been able to obtain an estimate of the relationship
between sales and the amount spent on promotion in these two media:
s = 2x1
2 – 10x2
2 – 2x1x2 + 18x1 + 34x2
s.t. x1 + x2 = 2
Solve.