Canning Transport wants to move goods from three (3) factories to three (3) distribution
centers. Information about the move is given below:
Shipping costs are (in $):
According to the Vogel’s Approximation Method, the initial solution would give to cell
CII a loading of ________.
An aggressive advertising campaign increases demand for the service by 50%. By what
percentage do the average queue length and average time in queue increase?
The international man of mystery knew the finest haberdashers the world over and
constantly sought to expand his dazzling array of fine suits, ties, and cufflinks. Closet
space was at a premium however, so purchases were carefully weighed. Each suit
provides 23 units of dazzlement, each tie 14, and a set of cufflinks is worth an easy 8. A
suit takes up 0.5 cubic feet of closet space and $900 of budget. A tie costs $135 and
cufflinks cost $100 per set. Cufflinks are tiny even in the original box, they take up only
.01 cubic feet while ties occupy a lusty .25 cubic feet. He has budgeted $12,000 for
clothes on this trip and has 20 cubic feet of closet space left to fill.
Formulate an objective function and constraints to model this situation.
Whereas the maximization primal model has ≤ constraints, the ________ dual model
has ≥ constraints.
The linear programming problem whose output follows determines how many red nail
polishes, blue nail polishes, green nail polishes, and pink nail polishes a beauty salon
should stock. The objective function measures profit; it is assumed that every piece
stocked will be sold. Constraint 1 measures display space in units, constraint 2
measures time to set up the display in minutes. Constraints 3 and 4 are marketing
restrictions.
MAX 100x1 + 120x2 + 150x3 + 125x4
Subject to 1. x1 + 2x2 + 2x3 + 2x4 ≤ 108
2. 3x1 + 5x2 + x4 ≤ 120
3. x1 + x3 ≤ 25
4. x2 + x3 + x4 > 50
x1, x2, x3,x4 ≤ 0
Optimal Solution:
Objective Function Value = 7475.000
Objective Coefficient Ranges
Right Hand Side Ranges
By how much can the profit on green nail polish increase before the solution would
change?
The model was entered into an Excel spreadsheet and the table below shows the answer
report in its entirety. Show how the profit is calculated.
Refer to the table below to answer the question(s) that follow:
What is the probability that the critical path for this project will be completed within 75
weeks?
The branch and bound method can be used for ________ integer problems except only
variables with integer restrictions are rounded down to achieve an initial lower bound
and only integer variables are branched on.
Refer to the figure below to answer the following questions.
Figure 3
Consider the network diagram given in Figure 3 with the indicated flow capacities
along each branch. What is the objective function for the 0-1 integer linear
programming formulation of the maximal flow problem?
The ________ solution area is an area bounded by the constraint equations.
Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is
the quality of care the pets receive, including well balanced nutrition. The kennel’s cat
food is made by mixing two types of cat food to obtain the “nutritionally balanced cat
diet.” The data for the two cat foods are as follows:
Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at
least 3 ounces of fat per day. What is the cost of this plan, and how much fat and protein
do the cats receive?
The Dean’s Office keeps tracks of student complaints received each week. The
probability distribution for complaints can be represented as a table as shown below.
The random variable xirepresents the number of complaints, and p(xi) is the probability
of receiving xi complaints.
What is the average number of complaints received per week?
When the ________ command is used in an Excel spreadsheet, all the values in a
column (or row) are multiplied by the values in another column (or row) and then
summed.
Use the following table to answer the question(s) below.
What decision should be made by the conservative decision maker?
Nathan enters the final exam period needing to pull off a miracle to pass his three
toughest classes, Healthy Life Choices, Success Central, and Walking Fitness. Naturally
he would also prefer to expend as little effort as possible doing so and as luck would
have it, he knows a guy that can help optimize his time and GPA using the magic of
management science. The model they develop is built around the notion of time spent
studying and doing all the assignments he has neglected throughout the semester. The
model is as follows, where S represents time spent studying (in minutes) and A
represents time spent making up assignments (also in minutes).
Maximize Z = 6S + 4A
subject to:
HLC 12S+10A ≥ 100
SC 6S + 8A ≥ 64
W 7S – 3A ≥ 36
Graphing was never one of Nathan’s strengths, so it is up to you to develop a graphical
solution to his problem and advise him on how much time should be invested in
studying and how much time should be spent catching up on assignments.
A professor’s son, having made the wise decision to drop out of college, has been
finding his way in life taking one job or another, leaving when his creativity is overly
stifled or the employer tires of his creativity. The professor dutifully logs the duration of
his son’s last few careers and has determined that the average duration is normally
distributed with a mean of sixty six weeks and a standard deviation of ten weeks. The
next career begins on Monday; what is the likelihood that it endures for less than a year
and a half?