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A newsboy sells newspapers and his goal is to maximize profit. He kept a record of his
sales for 125 days with the following result:
His ordering policy is to order an amount each day that is equal to the previous day's
demand.
A newspaper costs the carrier 50 cents and he sells it for $1.00. Unsold papers are
returned and he receives 25 cents (for a loss of 25 cents).
Develop the cumulative distribution table and the corresponding random numbers.
Given this model
Maximize Z = 6S + 4A
subject to:
12S + 10A ≥ 100
6S + 8A ≥ 64
7S - 3A ≥ 36
What is the optimal solution and the surplus associated with the first constraint?
This model was run in Excel and a portion of the answer report appears below. Provide
an interpretation that includes the revenue realized from the production run.
Variable Cells
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. Determine the maximal flow on the following path: node 1 to node
2 to node 7 to destination node 9.
Given the following linear programming problem:
maximize 4x1 + 3x2
subject to 4x1 + 3x2 ≤23
5x1 - x2 ≤ 5
x1, x2 ≥ 0
What is the optimal value of this objective function?
A Markov process for two states has the following transition matrix:
A B
A 0.35 0.65
B 0.42 0.58
Assume that we start with state 1, what is the probability matrix of the system being in
state A or B in period 3 given the system started in state B?
A ________ breaks down a project into modules: subcomponents, components,
activities, and tasks.
An investor is consider four different opportunities, A, B, C, or D. The payoff for each
opportunity will depend on the economic conditions, represented in the payoff table
below.
Economic Condition
Poor Average Good Excellent
Investment (S1) (S2) (S3) (S4)
A 50 75 20 30
B 80 15 40 50
C -100 300 -50 10
D 25 25 25 25
What decision would be made under maximax?
Mary Schultz is the incumbent Senator from Ohio and John Henderson is her opponent
in the upcoming election. Since Mr. Henderson is seeking to unseat Ms. Schultz, he is
on the offensive, while Ms. Schultz hopes to minimize his gains or her losses in the
election. The following payoff table shows the various percentage point gains/losses in
the polls for the two candidates based on their selection of certain political strategies.
Determine the optimal strategy and the optimal payoff for both players.
Andy Tyre manages Tyre's Wheels, Inc. Andy has received an order for 1000 standard
wheels and 1200 deluxe wheels for next month, and for 750 standard wheels and 1000
deluxe wheels the following months. He must fill all the orders. The cost of regular
time production for standard wheels is $25 and for deluxe wheels, $40. Overtime
production costs 50% more. For each of the next two months there are 1000 hours of
regular time production and 500 hours of overtime production available. A standard
wheel requires .5 hour of production time and a deluxe wheel, .6 hour. The cost of
carrying a wheel from one month to the next is $2.
Write the constraints for this problem.
Zevon Enterprises
Zevon Enterprises provides services for clients worldwide and to protect all parties to
this course as well as Zevon, we shall refer to those services as X1, X2, and X3. Each of
these services has its own special mix of needs for the resources the company has at its
disposal. The X1 product requires three lawyers, seven guns, and $6,000; the X2
product requires two lawyers, five guns, and $4,000; and the X3 product requires four
lawyers, six guns, and $7,000. Zevon has access to 5,000 lawyers, 10,000 guns, and
$15,000,000. For ease of conversation, Zevon employees usually speak about dollars as
"per thousand" so one of them asking for $7 means that they really need $7,000.
Zevon's demand is variable depending on what they charge for it. For example, the X1
product's demand is 200 - 2.25p1. The demand for X2 is 300 - 3p2, and the demand for
X3 is 400 - 3.5p3. The per unit profit forX1 through X3 can be calculated by subtracting
the per unit cost from the sales price, so for X1, the profit is p1 - 25, for X2 the profit is
p2- 3, and for X3 the profit is p3- 3.5.
Formulate the objective function and constraints for this scenario.
If X has the following probability distribution
X 1 2 3 4
P(X) .1 .5 .2 .2
Compute the expected value of X.
The following data summarizes the historical demand for a product:
If the forecasted demand for June, July, and August is 32, 38 and 42, respectively, what
is MSE?
A bakery's use of corn syrup is normally distributed with a mean of 50 gallons per day
and a standard deviation of 5 gallons per day. Lead time for delivery of the syrup is
normal with a mean of 4 days and a standard deviation of 2 days. The manager wants a
service level of 99 percent. Calculate the reorder point.
Consider the following annual sales data for 2001-2008:
Calculate the coefficient of determination.
Max Z = 3x1 + 5x2
Subject to: 7x1 + 12x2 ≤ 136
3x1 + 5x2 ≤ 36
x1, x2 ≥ 0 and integer
Find the optimal solution.
A rendering plant wishes to use the data (sales records from a few local businesses and
the month of the year) to help determine their supply level for the coming months. The
records shown in the table provide an excellent opportunity for you to assist them with
their forecasting.
What is the regression equation resulting from using Sales to forecast Pounds?
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. Determine the annual ordering cost and carrying cost if the
optimal production quantity is made each time.
If a student attends every management science class, the probability of passing the
course is 0.80; but if the student only attends randomly, then the probability of passing
the course is 0.50. If a student fails, he or she can take a makeup exam where the
probability of passing is 0.60 if the student has attended every class. This probability of
passing the makeup exam drops to 0.10 if the student has attended at random.
Passing the course is worth 5 credits. Full time attendance "costs" 3 credits in terms of
energy and time, whereas random attendance "costs" only 1 credit.
Use a decision tree to decide which is the best attendance pattern to adopt. Assume that
all failing students take the make up exam and that the payoff for failing is equal to 0.
