1) In the term linear programming, the word programming comes from the phrase
“computer programming.”
2) In a second order exponential smoothing, a low gives less weight to more recent
trends.
3) In Markov analysis, the transition probability Pij represents the conditional
probability of being in state i in the future given the current state of j.
4) The advantage of simulation over queuing or waiting line models is that simulation
allows us to relax our assumptions regarding arrival and service distributions.
5) The F distribution is a continuous probability distribution that is helpful in testing
hypotheses about variances.
6) Slack and surplus variables are used in simplex only for the solution of maximization
problems.
7) A probability is a numerical statement about the chance that an event will occur.
8) Shadow prices are the positives of the numbers in the Cj – Zj row’s slack variable
columns.
9) If we roll a single die twice, the probability that the sum of the dots showing on the
two rolls equals four (4), is 1/6.
10) In a transportation problem, a single source may supply something to all
destinations.
11) The Hungarian method is designed to solve transportation problems efficiently.
12) Customers enter the waiting line to pay for food as they leave a cafeteria on a
first-come, first-served basis. The arrival rate follows a Poisson distribution, while
service times follow an exponential distribution. If the average number of arrivals is
four per minute and the average service rate of a single server is seven per minute, what
proportion of the time is the server busy?
A) 0.43
B) 0.57
C) 0.75
D) 0.25
E) 0.33
13) With an annual demand of 2,400 units, daily demand of 10 units, and daily
production rate of 40 units, a company has determined that each production run will be
for 200 units. If production starts when the inventory level is at zero, how many units
would actually be in the warehouse at the end of the first day of production? (Round
your answer to the nearest unit.)
A) 12
B) 20
C) 30
D) 40
E) None of the above
14) Reducing the overall activity time is based on which of the following steps?
A) crashing activities with the lowest overall crash cost
B) crashing activities with the lowest overall normal cost
C) crashing activities on the critical path based on lowest overall cost
D) crashing activities on the critical path based on lowest cost/week
E) crashing activities with the lowest cost/week
15) The annual demand for a product has been projected at 2,000 units. This demand is
assumed to be constant throughout the year. The ordering cost is $20 per order, and the
holding cost is 20 percent of the purchase cost. Currently, the purchase cost is $40 per
unit. There are 250 working days per year. Whenever an order is placed, it is known that
the entire order will arrive on a truck in 6 days. Currently, the company is ordering 500
units each time an order is placed. What should be the reorder point (excluding any
safety stock) under the current policy?
A) 48
B) 100
C) 6
D) 24
E) None of the above
16) In applying the simplex solution procedure to a minimization problem to determine
which variable enters the solution mix,
A) pick the one with the most positive .
B) pick the one with the largest Cj.
C) pick the one with the smallest Zj.
D) pick the one with the most negative .
E) pick the smallest nonnegative number formed by dividing each amount in the
quantity column by the appropriate column at the exiting variable.
17) A transformation describes
A) the relationship between stages.
B) the initial condition of the system.
C) a stage.
D) a state variable.
E) None of the above
18) Given the following data and seasonal index:
(a) Compute the seasonal index using only year 1 data.
(b) Determine the deseasonalized demand values using year 2 data and year 1’s seasonal
indices.
(c) Determine the trend line on year 2’s deseasonalized data.
(d) Forecast the sales for the first 3 months of year 3, adjusting for seasonality.
19) At the start of football season, the ticket office gets busy the day before the first
game. Customers arrive at the rate of four every ten minutes. A ticket seller can service
a customer in four minutes. Traditionally, there are two ticket sellers working. The
university is considering an automated ticket machine similar to the airlines’ e-ticket
system. The automated ticket machine can service a customer in 2 minutes.
(a) What is the average length of the queue for the in-person model?
(b) What is the average length of the queue for the automated system model?
(c) What is the average time in the system for the in-person model?
(d) What is the average time in the system for the automated system model?
(e) Assume the ticket sellers earn $8 per hour and the machine costs $20 per hour
(amortized over 5 years). The wait time is only $4 per hour because students are patient.
What is the total cost of each model?
20) Table 14-2
The following data consists of a matrix of transition probabilities (P) of three competing
retailers, the initial market share (0). Assume that each state represents a retailer
(Retailer 1, Retailer 2, Retailer 3, respectively) and the transition probabilities represent
changes from one month to the next.
Using the data given in Table 14-2, find the market shares for the three retailers in
month 1.
A) (1) = (0.09, 0.42, 0.49)
B) (1) = (0.55, 0.33, 0.12)
C) (1) = (0.18, 0.12, 0.70)
D) (1) = (0.55, 0.12, 0.33)
E) (1) = (0.33, 0.33, 0.33)
21) As part of a larger problem, you are trying to determine whether or not to open a
plant with a capacity of 10,000 units (using binary variable Y). You also define X as the
number of units (if any) produced at that plant. How will you ensure that Y will equal 1
if the plant is open?
A) Y >= X
B) Y =< X
C) X + Y >= 2
D) X = 10000Y
E) X =< 10000Y
22) Which of the following statements is false concerning goal programming?
A) The objective function is the main difference between linear programming and goal
programming.
B) The objective in goal programming is to minimize deviational variables.
C) Deviational variables are zero if a goal is completely obtained.
D) It is not possible for two goals to have equal priority.
E) The priorities of each goal are reflected in the objective function.
23) Utility values typically range from
A) -1 to 1
B) 1 to 10
C) 0 to 1
D) 1 to 100
E) None of the above
24) The number of cell phone minutes used by high school seniors follows a normal
distribution with a mean of 500 and a standard deviation of 50. What is the probability
that a student uses fewer than 600 minutes?
A) 0
B) 0.023
C) 0.841
D) 0.977
E) None of the above
25) Calculate (a) MAD, (b) MSE, and (c) MAPE for the following forecast versus
actual sales figures. (Please round to four decimal places for MAPE.)
26) A company is producing cylindrical blocks for a children’s toy. The average
diameter of a block is 3.5 inches. Sixteen blocks are inspected and the diameters are
measured. The standard deviation is estimated to be 0.02 inches. What are the 99.7%
upper and lower control limits for the x-bar chart?
27) The demand for refrigerators at an appliance store adheres to the following
probability distribution:
The store orders 4 refrigerators per day to have in stock to meet demand. They are
trying to maintain low inventory levels. The holding cost is $5/unit/day. The ordering
cost is $20 per order. The lost sale cost is $10/unit. A simulation is to be developed to
estimate the average daily inventory cost over 5 days. The table below shows the
random numbers to be used for refrigerator demand and lead time on orders:
Assuming that beginning inventory is equal to 5 with no prior orders in transit, what is
the overall average daily cost of inventory for the 5 days?
28) In PERT/CPM, what is meant by the critical path?
29) There is a 60% chance that a customer without a smart phone will buy one this year.
There is a 95% chance that a customer with a smart phone will continue with a smart
phone going into the next year. If 30% of target market currently own smart phones,
what proportion of the target market is expected to own a smart phone next year?
30) As a supervisor of a production department, you must decide the daily production
totals of a certain product that has two models, the Deluxe and the Special. The profit
on the Deluxe model is $12 per unit, and the Special’s profit is $10. Each model goes
through two phases in the production process, and there are only 100 hours available
daily at the construction stage and only 80 hours available at the finishing and
inspection stage. Each Deluxe model requires 20 minutes of construction time and 10
minutes of finishing and inspection time. Each Special model requires 15 minutes of
construction time and 15 minutes of finishing and inspection time. The company has
also decided that the Special model must comprise at most 60 percent of the production
total.
Formulate this as a linear programming problem.
31) Table 10-7
32) Interpret the consistency ratio.
33) There is a 30% chance that any current client of company A will switch to company
B this year. There is a 20% chance that any client of company B will switch to company
A this year. If these probabilities are stable over the years, and if company A has 1000
clients and company B has 1000 clients, in the long run (assuming the probabilities do
not change), what will the market shares be?
34) What is meant by a multiphase system?
35) For each qualitative variable, the number of dummy variables must equal ________
the number of categories of the qualitative variable.