The derivative of a function equals the slope of the curve defined by that function.
The first step in formulating a linear programming model is to define the objective
function.
The branch and bound method is a solution approach that partitions the feasible solution
space into smaller subsets of solutions.
The simplex method does not guarantee an integer solution.
Seasonal patterns are observed only during the four seasons – winter, spring, summer,
and fall.
Slack variables are added to constraints and represent unused resources.
The slope of a curve at its highest point equals 1.
Sensitivity analysis allows the modeler to relax the certainty assumption.
Product mix problems cannot have greater-than-or-equal-to (≥) constraints.
At least one or both deviational variables in a goal constraint must equal 0.
Assumptions of the basic EOQ model include constant demand, no shortages, constant
lead time, and instantaneous replenishment.
Both linear and nonlinear programming models have the general form of an objective
function subject to more than 1 constraint.
Random numbers are equally likely to occur.
The standard deviation of project duration is the average of the standard deviation of all
activities on the critical path.
In a transshipment problem, items may be transported from one source to another.
The shortest route network problem could help identify the best plan for running cables
for televisions throughout a building.
In the classic game show Password, the suave, silver-haired host informed the
contestants, “you can choose to pass or to play.” This expression suggests a mixed
integer model is most appropriate.
The choice of the initial node in the minimal spanning tree technique must be the first
node.
In a periodic inventory system, a constant amount is ordered when inventory declines to
a predetermined level.
Decision variables cannot be multiplied by each other in the objective function of a
nonlinear program.
Networks may be used to represent assignment problems.
The shortest route problem is to find the shortest distance between an origin and various
destination points.
The three types of integer programming models are total, 0-1, and mixed.
The sensitivity range for a constraint quantity value is the range over which the optimal
values of the decision variables do not change.
Probabilistic techniques assume that no uncertainty exists in model parameters.
A decision tree is a diagram consisting of circular decision nodes, square probability
nodes, and branches.
The events in an experiment are mutually exclusive if only one can occur at a time.
The basic types of forecasting methods include time series, regression, and qualitative
methods.
A variable is a value that is usually a coefficient of a parameter in an equation.
A joint probability is the probability that two or more events that are mutually exclusive
can occur simultaneously.
Developing the cumulative probability distribution helps to determine random number
ranges.
A set of events is collectively exhaustive when it includes all the events that can occur
in an experiment.
Conditional probabilities are shown in Venn diagrams.
A continuous random variable may assume only integer values within a given interval.
The variance of a discrete random variable is always greater than or equal to zero.
It’s time to buy pet food again and Lisa heads to the grocery store with $40 in her purse,
leaving her seven hungry cats and four hungry dogs at home. Dog food costs $1 per can
and cat food costs $0.50 per can. Dogs eat two full cans of food each day but cats eat
only one can. Lisa would like to buy enough food to last through her three-day
weekend. What is one appropriate constraint for this scenario?
A) 7C + 4D ≥ 3
B) 1C + 2D ≤ 40
C) .5C + 1D ≤ 40
D) 7C + 4D ≥ 1.5
In synthesization, decision alternatives are prioritized ________ criteria/ion.
A) within some
B) among some
C) among all
D) within each
After plowing through contracts for a decade, the contract writer knew about how long
it took to crank out the material necessary to satisfy a contract’s requirements. The
distribution could be modeled using the data provided in this table.
Using the random number table 14.3 in your text, column 1, reading across row 2, what
is the standard deviation of the average length of the next five contracts?
A) 0.50
B) 0.55
C) 0.60
D) 0.63
In determining the pairwise comparison matrix, if the decision maker rates the option A
compared to option B as “4”, then option B compared to option A:
A) would also have to be answered by the decision maker.
B) is also 4.
C) is 1/4.
D) is 2.
William ran the model in Excel and received both an answer and sensitivity report.
Which of these statements about this portion of the sensitivity report is best?
A) William needs 73 hours to produce.
B) William income cannot be determined from this report.
C) William has 7.5 pounds of sugar more than he needs.
D) William has 2.5 bushels of corn left over.
The use of simulation to analyze airport operations, and fire or police department
operations are known as:
A) public service operation.
B) environmental and resource analysis.
C) cost benefit analysis.
D) operations management.
A ________ probability is the altered marginal probability of an event based on
additional information.
A) marginal
B) conditional
C) posterior
D) none of the above
The transportation method is a linear programming technique where linearity can be
found in which of the following ways?
A) The cost of goods shipped from any source to any destination is a linear function of
quantity shipped.
B) The total cost associated with a given plan is a linear function of shipping costs.
C) Cell evaluations assume linear movements through the matrix.
D) The cost of goods shipped from any source to any destination is a linear function of
the cost per unit.
Multiple optimal solutions can occur when the objective function is ________ a
constraint line.
A) unequal to
B) equal to
C) perpendicular to
D) parallel to
Which of the following are assumptions or requirements of the transportation problem?
A) There must be multiple sources.
B) Goods are the same, regardless of source.
C) There must be multiple destinations.
D) There must be multiple routes between each source and each destination.
After calculating the EOQ and informing their supplier of their order amount, they are
informed that the supplier is reluctant to break a case, that is, there are 10,000 swizzle
sticks in a case and they must be ordered in multiples of that amount. Not wanting to
understock, the krewe decides to round up to the next highest multiple of 10,000. What
is their total inventory policy cost (excluding cost of goods) if they order at this
amount?
A) $936.75
B) $425.50
C) $418.93
D) $209.46
A transportation table contains an optimal solution when all the empty cell evaluations
are:
A) positive or 0.
B) negative or 0.
C) positive.
D) negative.
Slack variables are added to ________ constraints and represent unused resources.
A) ≤
B) <
C) ≥
D) >
E) =
Two companies are about to make a decision regarding an investment in a new
promotional campaign. Company A will either advertise in all media or advertise in
newspapers only. Company B will either run a sweepstake or run a big sale. The payoff
matrix is shown below.
Based on the information above, determine the proportion of time that Company A
should employ each strategy.
A) A1: 12.5%, A2: 87.5%
B) A1: 25%, A2: 75%
C) A1: 37.5%, A2: 62.5%
D) A1: 50%, A2: 50%
E) A1: 62.5%, A2: 37.5%
Quickbrush Paint Company is developing a linear program to determine the optimal
quantities of ingredient A and ingredient B to blend together to make oil-base and
water-base paint. The oil-base paint contains 90 percent A and 10 percent B, whereas
the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has
10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and
cannot obtain more at this time. Assuming that x represents the number of gallons of
oil-base paint, and y represents the gallons of water-base paint, which constraint is
correctly represents the constraint on ingredient A?
A) .9A + .1B ≤ 10,000
B) .9x + .1y ≤ 10,000
C) .3x + .7y ≤ 10,000
D) .9x + .3y ≤ 10,000
The local soda machines union has some concerns regarding how busy these two
machines are during the day. The union has work rules that demand that machines can
be no busier than working two-thirds of their scheduled work shift. How many
machines should they demand management add to the work force to bring them in line
with the utilization rule?
A) 3 machines
B) 2 machines
C) 1 machine
D) none – they are already at that figure
Greg, a young entrepreneur, has developed an aggressive business plan and is
presenting his profit projections on the popular show Shark Tank in hopes of securing
some venture capital. He concludes his presentation with an LP model of his planned
product mix, and is convinced he will seal the deal by demonstrating that his profits are
limitless since his LP model is unbounded. What should the sharks tell him?
A) “Limitless profits sound fantastic, here’s a blank check.”
B) “Limitless profits are possible only in minimization models, and we want you to
maximize profits.”
C) “Unlimited profits aren’t possible. You must have made a mistake in your LP model.”
D) “Limitless profits are possible only in maximization models, and we want you to
minimize profits.”
The Taco Barn
After tallying the receipts for their first year of operation, the owners of the Taco Barn
are encouraged. Sales of their artisnal tacos, made from such exotic ingredients as
ground beef, cheese, and beans, have been strong and seem to give hope to the coming
year. Taco sales by month are shown in the table.
Armed only with his fingers, the owner decides that the safest forecasting approach is a
weighted moving average using 0.6, 0.3, and 0.1 for the most recent three. His fingers are
aching by the time he reaches May and he is worried about his ability to stuff tacos during
tomorrow’s dinner rush. Help him out by finding the forecast for June.
A) 583.5
B) 573.9
C) 636.3
D) 673
A list of the tasks, broken down into modules, components, and individual tasks, is
called a
A) work breakdown structure (WBS).
B) PERT.
C) planning matrix.
D) critical path.
The transportation method assumes that:
A) the number of rows is equal to the number of columns.
B) there must be at least 2 rows and at least 2 columns.
C) both A and B
D) the product of rows minus 1 and columns minus 1 should not be less than the
number of completed cells.
The problem that deals with the distribution of goods from several sources to several
destinations is the:
A) network problem.
B) assignment problem.
C) transportation problem.
D) transshipment problem.
Which of the following will not decrease system utilization?
A) increase in arrival rate
B) increase in service rate
C) increase in the number of servers
D) decrease in service time
If the price increases, but fixed and variable costs do not change, the break-even point:
A) decreases.
B) increases.
C) remains the same.
D) may increase or decrease, depending on sales.
Which of these disciplines typically does not fall under the umbrella of analytics?
A) information systems
B) statistics
C) management science
D) operations management
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.
The father had built his fortune as a real estate speculator and now devoted his energies
to his new passion, pessimism. Which alternative would be the best choice given this
new hobby?
A) A
B) B
C) C
D) D
The field of management science:
A) approaches decision making irrationally with techniques based on the scientific
method.
B) is another name for management or human resources management.
C) concentrates on the use of quantitative methods to assist managers in decision
making.
D) is completely separate and distinct from all other disciplines.
Project Sand Mandala
Carrie meticulously calculated the early and late start and finish times for her latest
project and recorded them using different colors of sand on a pristine slab of white
marble. She used red for late start and late finish times and green for early start and
early finish times. Activity durations and their identifiers were written with black sand.
She finished her task and had an opportunity to admire her work only briefly before a
colleague came by and swept most of it away. Sadly, this was before Carrie could
record the numbers on a more permanent medium, so now she turns to you to help.
Joe used a project management software package and has determined the following
results for a given project:
Expected completion time of the project = 22 days
Variance of project completion time = 2.77
What is the probability of completing the project over 20 days?
A) 3849
B) 8849
C) 1151
D) 7642
The poultry farmer would like to generate 80 ounces of fertilizer per week while
feeding a maximum of 160 ounces of layer pellets each week. Which of these
constraints is correct?
A) 3L + 2C + 4C ≤ 80
B) 5L + 4C + 8B ≤ 160
C) 5L + 4C + 8B ≥ 160
D) 5L + 4C +8B ≥ 80
The linear programming model for a transportation problem has constraints for supply
at each ________ and ________ at each destination.
A) destination, source
B) source, destination
C) demand, source
D) source, demand
The XYZ manufacturing company produces ball bearings. The annual fixed cost is
$20,000 and the variable cost per ball bearing is $3. The price is related to demand
according to the following equation:
v = 1000 – 8p. What is optimal profit?
A) $6668
B) $7668
C) $8668
D) $9768
The transition matrix below shows the probabilities that customer switch between two
grocery stores, Don’s and Limmer’s, each week.
If a customer shopped at Don’s the first week, what is the probability that they are
shopping at Limmer’s the third week?
A) 0.17
B) 0.34
C) 0.66
D) 0.83
E) none of the above
Which of these statements is best?
A) An unbounded problem is also infeasible.
B) An infeasible problem is also unbounded.
C) An unbounded problem has feasible solutions.
D) An infeasible problem has unbounded solutions.
An art critic is evaluating four differerent interpretations of “The Nutcracker”. The
pairwise comparison matrix for the criterion “originality of choreography” is given
below.
Choreographer A B C D
A 1 1/3 3 4
B 3 1 5 2
C 1/3 1/5 1 6
D 1/4 1/2 1/6 1
Determine the priorities of the four choreographers relative to “originality.”
A) A is preferred to B; B is preferred to C; and C is preferred to D.
B) B is preferred to A; A is preferred to D; and D is preferred to C.
C) B is preferred to A; A is preferred to C; and C is preferred to D.
D) C is preferred to A; A is preferred to D; and D is preferred to B.
Consider the following linear programming problem:
MIN Z = 3x1 + 2x2
Subject to: 2x1 + 3x2 ≥ 12
5x1 + 8x2 ≥ 37
x1, x2 ≥ 0
What is minimum cost and the value of x1 and x2 at the optimal solution?
If lead time and demand are constant then ________ is zero.
The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer.
Wiethoff has four XOAXOAerent machines that can produce this kind of hose. Because
these machines are from XOAXOAerent manufacturers and use XOAXOAering
technologies, their specifications are not the same and not all four machines have to be
used to produce all of the garden hoses.
Give the constraints for the problem.
The drying rate in an industrial process is dependent on many factors and varies
according to the following distribution.
Determine the drying time for these 5 random numbers: 0.13, 0.09, 0.19, 0.81, and 0.12.
Consider a capital budgeting example with five projects from which to select. Let xi = 1
if project a is selected, 0 if not, for i = 1, 2, 3, 4, 5. Write the appropriate constraint(s)
for the following condition: If project 3 is chosen, project 4 must be chosen.
A company distributes repair parts for high-end appliances. The annual demand is
81,000 and the company operates 300 days per year. The annual carrying cost is 20% of
the item cost, which is $500. The ordering cost is estimated at $60 and the shortage cost
is $150.
Determine the optimal shortage level.
A product has an annual demand of 3600 units. Unit cost for this product is $3. Set up
cost is $20 and the inventory carrying rate as a percent of the unit cost is 25%. The
product is produced in-house where the daily production rate is 50 units. Assume 360
working days per year and determine the economic production quantity.
A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit
is $6 from cooperative A and $5.50 per unit from cooperative B. Develop an objective
function that would minimize the total cost.
Total revenue minus total cost equals ________.
Ashley’s manufactures home furnishings for department stores. Planning is underway
for the production of the following items during the next production period:
Quilts (x1) Blinds (x2) Pillows (x3)
Fabric required (yards) (d1) 7 4 9
Time required (hours) (d2) 1.5 2 0.5
Packaging material (ounces) (d3) 3 2 1
Profit (d4) 12 10 8
Ashley has 3000 yards of material in stock for this production period. Five hundred
hours of production time are scheduled and 400 ounces of packaging material is
available. Each of these quantities can be adjusted through overtime or extra purchases.
Ashley’s highest priority is to achieve a profit of $3200. Her second priority is to avoid
additional purchases of packaging material. Third, she wants to use all of the scheduled
production hours, and fourth, minimize any fabric remaining from the 3000 yards. Note
that the deviational variables associated with each item are given in the table.What is
the profit constraint?
12x1 + 10x2 + 8x3 + d4
Donuts Please
The number of donuts needed for department meetings at the start of the semester can
be modeled by the continuous probability distribution , which we can integrate
from 0 to some value x, which is the number of days before the actual beginning of the
semester.
What is the value for x when random number r is equal to six?
Determining where to build one way roads at the least cost within a park that takes
visitors to every popular sight and returns them to the entrance represents a ________
network model.
A crew of mechanics at the Department of Transportation garage make minor repairs to
snowplows during the winter. The snowplows break down at an average rate of 4
vehicles per day and breakdowns are distributed according to the Poisson distribution.
The mechanic can service an average of 7 vehicles per day with a repair time
distribution that approximates a negative exponential distribution. Assume an 8 hour
day.
On average, how long does a snowplow wait before the mechanic can begin his repair?
Centerville city council is in the process of developing city tax rates. The annual tax
base for real estate property is $750 million and for general sales, $80 million. Annual
local gas consumption is estimated at 12 million gallons. They have three goals, listed
in order of priority:
1)Tax revenues must be at least $25 million to meet the city’s financial commitments.
2)Sales tax cannot exceed 25% of all taxes collected.
3)Gasoline tax cannot exceed 8 cents per gallon.
Formulate as a goal programming problem.
then the objective function should be: Min P1d1
The first day on the cruise was a “day at sea” meaning no port of call, and only the
amenities onboard for amusement. Restless and uncomfortably full after seven trips
through the buffet, the management scientist gambled away most of his vacation money
at the onboard casino. The excursions would be a necessity, but now it became less
important to maximize the joy of the excursions and more vital to get off the boat as
cheaply as possible while still staying busy at the three pots of call. What is an
appropriate objective function for this modified cruise vacation?
There are 4 jobs in a 4 person office that must be done as quickly as possible. The
supervisor has used the assignment method to assign people to jobs, and has completed
the first step. She had to rush off to a meeting and has asked to assign the jobs to the
people before she returns. The original matrix which shows the expected completion
time for each person for each job, and the one she just completed are both shown below.
Which person should be assigned to which job? How long will the jobs take?
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:
If the company wanted to increase the available hours for one of their constraints
(assembly, painting, or inspection) by two hours, they should increase ________.
When supply exceeds demand, a dummy ________ is added to the solution tableau.