In a transshipment problem, items may be transported from sources through
transshipment points on to destinations.
In portfolio selection problems, risk is measured by the variance of the return on the
portfolio.
In a transshipment problem, items may be transported from one destination to another.
Blending problems usually require algebraic manipulation in order to write the LP in
‘standard form.”
The simplex method moves from one better solution to another until the best one is
found, and then it stops.
Regardless of the number of nodes in a network, the minimal spanning tree cannot
contain the two nodes with the greatest distance between them.
In most media selection decisions, the objective of the decision maker is to minimize
cost.
Moving averages are good for stable demand with no pronounced behavioral patterns.
Two concurrent activities in a project can be represented in an AOA network by starting
and ending on the same node.
An AON network will never require dummy activities.
In a continuous probability function, the area under the curve represents the probability
of occurrence of the random variable.
If lead time and demand are constant, safety stock is equal to demand multiplied by
lead time.
The terms in the objective function or constraints are multiplicative.
Shortage costs include loss of customer goodwill.
In an unbalanced transportation model, all constraints are equalities.
The Lagrangian function is diferentiated with respect to each variable, and the resulting
equations are solved simultaneously.
In a goal programming model, the terms in the objective function are summed to
determine the maximum profit or minimum cost.
An assignment problem is a special form of transportation problem where all supply
and demand values equal 1.
The noninstantaneous receipt model applies only to manufacturing.
A Markov assumption is that the probabilities are constant over time.
Constraints usually appear as equations that are less than, equal to, or greater than a
parameter.
Business analytics brings together the disciplines of information systems, management
science, statistics, and mathematical modeling.
The branch and bound method is a solution technique specifically limited to integer
programming problems.
If an integer programming problem has no feasible solution, then its LP relaxation
(relaxed solution) must also have no feasible solution.
In PERT, the expected project completion time is assumed to be distributed according to
a beta distribution.
The coefficient of determination provides a measure of how the level of the
independent variable in a regression equation explains the level of the dependent
variable in the equation.
In order to model a “prohibited route” in a transportation or transshipment problem, the
route should be omitted from the linear program.
In the simplex method, the model is put into the form of a table, and then a number of
mathematical steps are performed on the table.
In scoring models, the two alternatives with the highest scores are compared to make
the final decision.
In a classic blending problem, revenue is maximized by subtracting cost from profit.
Another name for the mean of a probability distribution is its expected value.
Unacceptable (prohibited) routes in a transportation problem are assigned cost values of
zero.
The shipping company manager wants to determine the best routes for the trucks to take
to reach their destinations. This problem can be solved using the minimal spanning tree.
Subjective probability is an estimate based on personal belief, experience, or knowledge
of a situation.
Regret and opportunity loss mean the same thing.
A periodic inventory system has constant order sizes and order intervals.
In using the branch and bound method, if a branch gives an infeasible solution to the
associated linear programming problem, then the particular branch is fathomed and is
not considered any further.
Transportation problems are solved manually within a tableau format.
If all of the assumptions for the basic EOQ model are met, the fixed-period model will
behave exactly like the EOQ model.
The critical path is the longest path through the project network.
The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has
a limited amount of the three ingredients used to produce these chips available for his
next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of
herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of
herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of
flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of
vinegar chips $0.50.What is the constraint for salt?
A) 6L + 8V ≤ 4800
B) 1L + 2V ≤ 4800
C) 3L + 2V ≤ 4800
D) 2L + 3V ≤ 4800
The manager of the Quick Stop Corner convenience store (which is open 360 days per
year) sells four cases of Stein soda each day (1440 cases per year). Order costs are
$8.00 per order. The lead time for an order is three days. Annual holding costs are equal
to $57.60 per case.If the manager orders 16 cases each time she places an order, what is
the average inventory level?
A) 4 cases
B) 8 cases
C) 12 cases
D) 20 cases
Armed only with his fingers, the owner decides that the safest forecasting approach is a
moving average of two periods. Generate a forecast for the year using this technique
and then calculate forecast errors using MSE. What is the mean squared error for this
forecasting approach?
A) 3049
B) 4045
C) 6024
D) 5011
Which of the following assumptions is not an assumption of the transportation model?
A) Shipping costs per unit are constant.
B) There is one transportation route between each source and destination.
C) There is one transportation mode between each source and destination.
D) Actual total supply and actual total demand must be equal.
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 eighty-eight weeks and a standard deviation of twenty
weeks. The next career begins on Monday; what is the likelihood that it endures for
more than one year?
A) 92%
B) 94%
C) 96%
D) 98%
In a zero sum game, one player’s gains represent another’s exact:
A) gains.
B) losses.
C) gains and losses.
D) gains or losses.
At Joe’s Pool Hall they rent tables by the hour and also rent Balabushka pool cues for
purists that can’t afford their own. The rental process for these cues is exhaustive and
takes an hour and a half for each application. There are three leasing agents that conduct
these interviews, and on average, it is one hour between customer arrivals.How busy
are the servers on average?
A) 50% utilized
B) 60% utilized
C) 70% utilized
D) 80% utilized
In a multiperiod scheduling problem, the production constraint usually takes the form
of:
A) beginning inventory + demand – production = ending inventory.
B) beginning inventory – demand + production = ending inventory.
C) beginning inventory – ending inventory + demand = production.
D) beginning inventory + demand + production = ending inventory.
________ are generally independent of the volume of units produced and sold.
A) Fixed costs
B) Variable costs
C) Profits
D) Average cost
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.The utilization is:
A) .30.
B) .45.
C) .57.
D) .85.
How would multiple optimal solutions typically appear on a graphical solution?
A) a point
B) a line
C) a plane
D) a cube
Variable cost:
A) depends on the number of units produced.
B) plus marginal cost equals fixed cost.
C) is equal to total cost in deterministic models.
D) is the same as average cost.
Jolt – M
The soda machines outside the lecture hall sees a steady stream of customers
throughout the day. Between the student’s use of the machine and the mechanism, it
takes 15 seconds (exponentially distributed) to deliver a can of carbonated sugar water
to a thirsty customer. Over the course of a twelve hour lecture day, students arrive at the
rate of 450 per hour.
It is precisely two minutes before class begins when Lisa decides to buy a soda. The
professor has a well-deserved reputation for locking out everyone that is even a second
late. Undeterred, Lisa makes a beeline for the machines, their eerie glow and soothing
hum calling to her almost as much as the promise of an ice cold beverage. “I’m pretty
sure I can make it,” she remarks to a classmate as she gets in line for a soda, “and if I’m
late, all I need to do is bat my eyelashes at him and he’ll open the door and even
apologize for shutting it in the first place.” What will be the result of Lisa’s decision to
purchase a soda before class?
A) Lisa will easily make it to her seat with a refreshing soda, entering the room twenty
seconds before class begins.
B) Lisa will march into the lecture hall triumphantly holding her soda aloft a full twelve
seconds before class begins.
C) Lisa will need to start batting those eyelashes, because she’s almost four seconds late
for class.
D) Lisa will need to shift those eyelashes into overdrive as she is more than fourteen
seconds late for class. However, at least she has a soda.
Cars arrive at a single-bay car wash at an average of 6 per hour according to the Poisson
distribution. The wash time is a constant 4 minutes. What is the average number of cars
in line?
A) .022
B) .133
C) .267
D) .667
The U.S. Department of Agriculture estimates that the yearly yield of limes per acre is
distributed as follows:
The estimated average price per bushel is $16.80.
What is the expected yield of the crop?
A) 425
B) 442
C) 440
D) 475
Which of the following is not an assumption or a characteristic of a Markov Process?
A) The transition probabilities are the same for any customer.
B) The transition probabilities will remain constant over time.
C) The probability of being in a particular state at any one time period depends only on
the state immediately preceding it.
D) In a transition matrix, sum of the row probabilities must sum to one.
E) In a transition matrix, sum of the column probabilities must sum to one.
The majority of the goal constraints are equalities that include ________ variables.
A) only deviational
B) deviational and decision
C) only decision
D) neither deviational nor decision variables
If the price decreases, 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.
The following data represents quarterly sales of lawnmowers.
What is the seasonal index for the third quarter? (Round to the nearest hundredth.)
A) .20
B) .22
C) .26
D) .30
Consider the following constraint: 2x1 + 3x2 =60. Assume that we convert this
constraint into a goal constraint with the value of x1 = 15 and the value of x2 = 15. Then
the values of d1
+ and d1
– are ________ and ________, respectively.
A) 0, 15
B) 15, 0
C) 20, 0
D) 0, 20
Variable cost does not include:
A) raw materials and resources.
B) staff and management salaries.
C) material handling and freight.
D) direct labor and packaging.
An objective function:
A) shows where the break-even point is.
B) describes how much of a resource can be used.
C) can represent costs or profits.
D) describes something to be maximized.
Dinnertime
A professor is planning an informal gathering for 100 or so of his closest friends. The
project breaks down as follows:
What is the late start time for the Stock wine cellar activity?
A) 12
B) 17
C) 20
D) 24
The slope of the line labeled “A” in the diagram is:
A) order rate.
B) rate of inventory demand.
C) production rate.
D) production rate minus rate of inventory demand.
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of
stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The
investor has up to $50,000 to invest.
The investor stipulates that stock 1 must not account for more than 35% of the number
of shares purchased. Which constraint is correct?
A) X1 ≤ 0.35
B) X1 = 0.35 (50000)
C) X1 ≤0.35(X1 + X2 + X3)
D) X1 =0.35(X1 + X2 + X3)
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 annual ordering cost?
A) 2711.09
B) 1059.03
C) 1355.55
D) 495.74
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 exactly two of the
instances were the dutiful work of the male cats?
A) .273
B) .187
C) .429
D) .314
The Cruise
Their cruise would port out of New Orleans and promised seven days with a panoply of
excursions in Jamaica, Cozumel, and Grand Cayman. A list of excursions at each site
and key features of each appear in the table. The excursions were all day affairs, so it
was possible to engage in only one per port. The cruise ship sailed at night and docked
at each of these three ports at the crack of dawn. By dinner time, the ship was on its
way to the next port and next set of excursions. The couple was energetic and active for
a pair of 52 year-olds., and while enjoying an upper middle class lifestyle, they didn’t
want to spend money on excursions that might be better spent on tacky souvenirs. The
couple therefore budgeted $250 for the excursions the prices shown are per couple, so
for example, the $60 will pay for both of them to fill up on jerk chicken and mannish
water.
For each of the duplicate excursions (e.g., snorkeling is offered in all three ports), the
couple researched the quality of the activity and ranked the excursion among the
available alternatives, with higher numbers indicating better quality. Thus, snorkeling in
Jamaica is better than in Cozumel, and snorkeling in Cozumel is better than in Grand
Cayman. For the unique experiences, i.e., the turtle farm, the default rating was the a 3 .
(Note – data used in this test question should not be construed as vacation advice.)
What is an appropriate objective function for this vacation?
A) Max Z = JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL +
GTu
B) Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe
+ 90GS + 60GP + 110GH + 130GL + 95GTu
C) Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP +
3GH + 1GL + 3GTu
D) Min Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP +
3GH + 1GL + 3GTu
Participants eligible for a retraining program can be in one of four states:
A – not in the training program
B – discharged
C – in training
D – employed
You are given the following transition matrix and the fundamental matrix.
Assume that there were initially 10 people not in the training program (State A) and 60
people who were in the training program (State C). How many people will end up being
discharged, and how many people will be employed?
When systematically formulating a linear program, the first step is to:
A) construct the objective function.
B) formulate the constraints.
C) identify the decision variables.
D) identify the parameter values.
A periodic inventory system:
A) uses fixed order sizes at variable time intervals.
B) normally requires a larger safety stock.
C) cannot be used if demand is variable.
D) is used to periodically manage inventory.
For some positive value of Z, the probability that a standard normal variable is between
0 and Z is 0.2910. The value of Z is:
A) 0.17.
B) 0.81.
C) 1.25.
D) 1.65.
The branch and bound method uses a tree diagram of ________ to organize the solution
partitioning.
A) branches
B) nodes
C) nodes and branches
D) none of the above
The following data represents quarterly sales of lawnmowers.
What is the seasonal index for the fourth quarter? (Round to the nearest hundredth.)
A) .20
B) .23
C) .25
D) .30
In a transportation problem, items are allocated from sources to destinations:
A) at a maximum cost.
B) at a minimum cost.
C) at a minimum profit.
D) at a minimum revenue.
Lenny, a graduate research assistant “moonlights” at the short order counter in the
student union snack bar in the evenings. He is the only one on duty at the counter
during the hours he works. Arrivals to the counter seem to follow the Poisson
distribution with a mean of 8 per hour. Each customer is served one at a time and the
service time follows an exponential distribution with a mean of 5 minutes.
On average, how busy are the servers and how likely is it that they have nothing to do?
Cranky Jerry’s Day Care wants to minimize their food cost while meeting the minimum
(and I mean bare minimum) guidelines for nutrition as set forth by the state. The best
approach would be to follow the example in this chapter for a(n) ________ problem.
A customer molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The
per unit contribution for the juice glasses (x1) is equal to 60 – 5x1, and the per unit
contribution for the cocktail glasses (x2) is 80 – 4 x2 for a total contribution of 60 x1 –
5x1
2 + 80x2 – 4x2
2. Demand requires that the production of juice glasses is twice the
production of cocktail glasses (x1 = 2x2). Write the objective function for this problem
which illustrates the technique of substitution.
20x2 – 24x2
Solve the following problem using the simplex method.
Minimize Z = 2x1 + 6x2
Subject to: 2x1 + 4x2 ≤ 12
3x1 + 2x2 ≥ 9
x1, x2 ≥ 0
The quality control manager for ENTA Inc. must decide whether to accept (A1), further
analyze (A2), or reject (A3) a lot of incoming material. Assume the following payoff
table is available. Historical data indicates that there is 30% chance that the lot is poor
quality (S1), 50 % chance that the lot is fair quality (S2), and 20% chance that the lot is
good quality (S3).
What action would you choose according to minimax regret criterion?
If the forecast is 14 and the actual value is 15, then the error this period is ________.
A(n) ________ forecast typically encompass a period longer than one year.
Assume price and demand are related by the following function: v = 200 – p. If fixed
cost = $10,000 and variable cost = $8, then the expression for profit is ________.
A graphical representation of a linear program is shown below. The shaded area
represents the feasible region, and the dashed line in the middle is the slope of the
objective function.
If this is a minimization, which extreme point is the optimal solution?
________ consist of models that are represented as diagrams rather than as strictly
mathematical techniques.
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.
If the daily demand is 67 and the lead time in days is 2, what is the reorder point?
Assume that a plant manager has to decide where to locate its warehouse. The decision
has been narrowed down to choices among the following three cities: Detroit,
Cleveland, and St. Louis. The following pairwise comparison matrix summarizes the
preferences of the plant manager.
Determine the normalized matrix.
In a ________ linear programming model, some of the solution values for the decision
variables are required to assume integer values and others can be integer or noninteger.
A manager has developed a payoff table that indicates the profits associated with a set
of alternatives under two possible states of nature.
Alt S1 S2
1 10 2
2 -2 8
3 8 5
If the manager uses minimax regret as the decision criterion, which of the alternatives
would she choose?
Kushie’s Coffee in Bangalore is a quaint establishment nestled near MG Road in the
central business district. It serves coffee and fruit cake to a clientele that has been
enjoying these products for over fifty years. The demand for coffee beans is 6600 cases
per year (each case has 24 ten-pound bags). It would be disastrous for them to run out
of coffee, so they keep a safety stock of 30 cases. The cases cost $4800 and it costs $5
per case to order coffee. As coffee is a perishable product, the holding cost is fairly high
at $40/case/year. The lead time to receive an order is seven days. Kushie’s is open 300
days a year.
What is the optimal order quantity for Kushie’s Coffee?
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
You are offered the chance to obtain more space. The offer is for 15 units and the total
price is 1500. What should you do?
Assume a nonlinear programming problem with a single constraint has been solved.
The value of the Lagrange multiplier is $0.75 and the value of the optimal profit (Z) is
$25. If the right-hand side of the constraint is increased from 38 to 42, the new value of
Z will be ________.