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Consider the two person zero sum game between players A and B given by the following pay-off table:
(Solved)
Consider the two person zero sum game between players A and B given by the following pay-off table:
Required:
i) Using the maximin and minimax values, is it possible to determine the value of the game? Give
reasons.
ii) Use graphical methods to determine optimal mixed strategy for player A and determine the
value of the game.
Date posted:
January 23, 2019
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Answers (1)
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Define the following terms used in game theory:
i) Dominance.
ii) Saddle point
iii) Mixed strategy
iv) Value of the game
(Solved)
Define the following terms used in game theory:
i) Dominance.
ii) Saddle point
iii) Mixed strategy
iv) Value of the game
Date posted:
January 23, 2019
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Answers (1)
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Explain the following terms as used in decision analysis.
a) Decision making under risk versus uncertainty.
b) Decision trees versus probability trees.
c) Minimax versus maximax criterion.
d) Pure...
(Solved)
Explain the following terms as used in decision analysis.
a) Decision making under risk versus uncertainty.
b) Decision trees versus probability trees.
c) Minimax versus maximax criterion.
d) Pure strategy versus mixed strategy games.
e) Games with more than two persons versus non zero-sum games
Date posted:
January 23, 2019
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Answers (1)
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An urban cable television company is investigating the installation of cable TV system in urban areas. The engineering department estimates the cost of the system...
(Solved)
An urban cable television company is investigating the installation of cable TV system in urban areas. The engineering department estimates the cost of the system (in present worth Sh.) to be Sh. 7 million. The sales department has investigated four pricing plans. For each pricing plan, the marketing division has estimated the revenue per household in present worth Sh. to be:
Date posted:
January 23, 2019
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Answers (1)
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A trust officer for a major banking institution is planning the investment of a USD 1 million family trust for the coming year. The trust...
(Solved)
A trust officer for a major banking institution is planning the investment of a USD 1 million family trust for the
coming year. The trust officer has identified a portfolio of stocks and another group of bonds that might be
selected for investment. The family trust can be invested in stocks or bonds exclusively, or a mix of the two.
This trust officer prefers to divide the funds in increments of 10 percent; that is, the family trust may be split
100 percent stocks /0 percent bonds, 90 percent stocks /10 percent bonds, 80 percent stocks /20 percent
bonds, and so on.
The trust officer has evaluated the relationship between the yields on the different investments and general
economic conditions. Her judgment is as follows:
1) If the next year is characterized by solid growth in the economy, bonds will yield 12 percent and stocks
20 percent.
2) If the next year is characterized by inflation, bonds will yield 18 percent and stocks 10 percent.
3) If the next year is characterized by stagnation, bonds will yield 12 percent and stocks 8 percent.
a) Formulate a payoff table where payoffs represent the annual yield, in dollars, associated with the
different investment strategies and the occurrence of various economic conditions
b) Determine the optimal investment strategy using the max-max, max-min, Hurwicz (
),
equally likely, and regret criteria.
c) Suppose that a leading economic forecasting firm projects P(solid growth)= 0.4, P(inflation)=0.25,
and P (stagnation)= 0.35. Use the expected value criterion to select the appropriate strategy.
d) What is the expected value with perfect information?
Date posted:
January 23, 2019
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Answers (1)
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The following table is a payoff table for a particular venture.
(Solved)
The following table is a payoff table for a particular venture.
Required:
a) Determine the decision alternative that maximizes expected payoff.
b) Determine expected value under certainty.
c) What is the expected value of perfect information?
Date posted:
January 23, 2019
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Answers (1)
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The following is a payoff table for a particular venture.
(Solved)
The following is a payoff table for a particular venture.
Determine the optimal decision using:
a) Max-min criterion.
b) Max-max criterion.
c) Min-max regret criterion.
d) Maximum expected payoff (assuming equal likelihood of states of nature).
Date posted:
January 23, 2019
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Answers (1)
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Kenya Canning Transport is to move goods from three factories situated in Thika, Naivasha and
Machakos. These goods will be distributed to Nairobi, Mombasa and Kisumu....
(Solved)
Kenya Canning Transport is to move goods from three factories situated in Thika, Naivasha and
Machakos. These goods will be distributed to Nairobi, Mombasa and Kisumu. Information about the
units (in kilograms) to be moved is given below:
Required:
i) Draw a network diagram for the above problem
ii) Set a linear programming model for this problem
NOTE: Do not solve.
Date posted:
January 14, 2019
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Answers (1)
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The TamuTamu products company ltd is considering an expansion into five new sales districts. The
company has been able to hire four new experienced salespersons. Upon...
(Solved)
The TamuTamu products company ltd is considering an expansion into five new sales districts. The
company has been able to hire four new experienced salespersons. Upon analysing the new
salesperson's past experience in combination with a personality test which was given to them, the
company assigned a rating to each of the salespersons for each of the districts .These ratings are as follows:
The company knows that with four salespersons, only four of the five potential districts can be covered.
Required:
i) The four districts that the salespersons should be assigned to in order to maximize the total of the
ratings
ii) Maximum total rating.
Date posted:
January 14, 2019
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Answers (1)
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a) A baker makes two products; large loaves and small round loaves. He can sell up to 280 of the large
loaves and up to 400...
(Solved)
a) A baker makes two products; large loaves and small round loaves. He can sell up to 280 of the large
loaves and up to 400 small round loaves per day. Each large loaf occupies 0.01m3 of shelf space, each small loaf occupies 0.008m3 of space, and there is 4m3 of shelf space available. There are 8 hours available each night for baking, and he can produce large loaves at the rate of 40 per hour, and small loaves at the rate of 80 per hour. The profit on each large loaf is Sh.5.00 and Sh.3.00 profit on the small round loaf.
Required:
In order to maximize profits, how many large and small round loaves should he produce?
b) Summarize the procedure for solving the kind of quantitative technique you have used to solve part (a) above.
Date posted:
January 11, 2019
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Answers (1)
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A company wishes to purchase additional machinery in a capital expansion program. Three types of machinesare to be purchased: A, B, and C. Machine A...
(Solved)
A company wishes to purchase additional machinery in a capital expansion program. Three types of machines
are to be purchased: A, B, and C. Machine A costs USD 25,000 and requires 200 square feet of floor space for its
operation. Machine B costs USD 30,000 and requires 250 square feet of floor space. Machine C costs USD 22,000 and
requires 175 square feet of floor space. The total budget for this expansion program is USD 350,000. The
maximum available floor space for the new machines is 4,000 square feet. The company also wishes to
purchase at least one of each machine.
Given that machines A, B, and C can produce 250, 260, and 225 pieces per day, the company wants to
determine how many machines of each type it should purchase so as to maximize daily output (in units) from
the new machines.
a) Explicitly define your decision variables and formulate the LP model.
b) Assess the validity of the four underlying LP assumptions for this problem.
c) Solve and analyse the problem using a computer package
Date posted:
January 11, 2019
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Answers (1)
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Solve the following problem using the simplex method:
(Solved)
(a) Solve the following problem using the simplex method:
b) Verify your solution by solving graphically and relate tableaux to specific corner points.
c) Determine the shadow prices and interpret their meaning.
Date posted:
January 11, 2019
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Answers (1)
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The number of plumbing repair jobs by Manji Plumbing Service in each of the last nine months in
Nakuru town are listed below:
Month---Jobs
March 353
April 387
May 342
June...
(Solved)
The number of plumbing repair jobs by Manji Plumbing Service in each of the last nine months in
Nakuru town are listed below:
Month---Jobs
March 353
April 387
May 342
June 374
July 396
August 409
September 399
October 412
November 408
Required:
Required:
a)
i) Forecast the number of repair jobs Manji Plumbing Service will perform in December. Use the
least squares method.
Note:
ii) What is your forecast for December using a three-period weighted moving average with weights of
0.6, 0.3, and 0.1. How does it compare with your forecast from part (i)
above? b)
i) What are the aims of time series analysis?
ii) Describe what a season is in the context of a time series and give some examples.
iii) Describe the stages in obtaining a time series trend using the method of semi averages.
iv) Why must forecasts be treated with caution?
Date posted:
January 11, 2019
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Answers (1)
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Find the moving average of the time series of quarterly production (in tons) of coffee in an Indian State as given below. After that, come...
(Solved)
Find the moving average of the time series of quarterly production (in tons) of coffee in an Indian State as given below. After that, come up with a trend line to approximate the production in future.
Production (in Tons)
Date posted:
January 11, 2019
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Answers (1)
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The following regression equation was calculated for class of 24 CPA II students.
Required:
a) Calculate the t ratio and the 95% confidence interval for each regression...
(Solved)
The following regression equation was calculated for class of 24 CPA II students.
Standard error (0.0190) (0.034) (0.018)
Where y=students score on a theory examination
x1 = Students rank (from the bottom) in high
school x2 = Students verbal aptitude score
x3 =A measure of students character
Required:
a) Calculate the t ratio and the 95% confidence interval for each regression coefficient.
b) What assumptions did you make in (a) above? How reasonable are they?
c) Which regressor gives the strongest evidence of being statistically discernible?
d) In writing up a final regression equation, should one keep the first regressor in the equation, or drop if?
Why?
Date posted:
January 1, 2019
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Answers (1)
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Unlisted plc hopes to achieve a Stock Market quotation for its shares. A profit forecast is necessary and, in order to achieve such a forecast,...
(Solved)
Unlisted plc hopes to achieve a Stock Market quotation for its shares. A profit forecast is necessary and, in order to achieve such a forecast, the company has experimented with a number of approaches. The following are details from a linear regression on the last 11 years profit figures:
x = years (expressed 1 to 11)
y = annual profit figures
You are required:
a) To obtain the simple least squares regression line of Y on X;
b) To use the line to estimate profit in each of the next two years;
c) To calculate the coefficient of determination for the line and to explain its meaning;
d) To calculate the standard error of the regression line and to use this to obtain the 95% confidence
interval for the line;
e) On the basis of the information given on your answer (a) to (d) to determine whether it is likely that the regression line will be a good estimator of profit.
Date posted:
December 14, 2018
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Answers (1)
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Two different models are available for the same machine. The production statistics (number of units
produced per hour) of these two models are given below. The...
(Solved)
Two different models are available for the same machine. The production statistics (number of units
produced per hour) of these two models are given below. The data was collected on different days.
Will you conclude that Model A and Model B have the same productivity?
Date posted:
December 8, 2018
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Answers (1)
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In each of the following three situations, use binomial, poisson, or normal distribution depending on which is the most appropriate.
In each case, explain why you...
(Solved)
In each of the following three situations, use binomial, poisson, or normal distribution depending on which is
the most appropriate.
In each case, explain why you selected the distribution and draw attention to any feature which supports or
casts doubt on the choice of distribution.
a) Situation 1:
The lifetimes of a certain type of electrical components are distributed with a mean of 800 hours and
standard deviation of 160 hours.
Required:
i) Identify situation 1.
ii) If the manufacturer replaces all the components that fail before the guaranteed minimum lifetime of
600 hours, what percentage of the components have to be replaced?
iii) If the manufacturer wishes to replace only 1% of the components that have the shortest life, what
value should be used as the guaranteed lifetime?
iv) What is the probability that the mean lifetime of a sample of 25 of these electrical components exceeds 850 hours?
b) Situation 2:
A green grocer buys peaches in large consignments directly from wholesaler. In view of the perishable
nature of the commodity, the green grocer accepts that 15% of the supplied peaches will usually be
unsaleable. As he cannot check all the peaches individually, he selects a single batch of 10 peaches on
which to base his decision of whether to purchase a large consignment or not. If no more than two of
these peaches are unsatisfactory, the green grocer purchases the consignment.
Required:
i) Identify situation 2.
ii) Determine the probability that under normal supply conditions, the consignment is purchased.
c) Situation 3:
Vehicles pass a certain point on a busy single-lane road at an average rate of two per 10 second interval.
Required:
i) Identify situation 3.
ii) Determine the probability that more than three cars pass this point during a 20 second interval.
Date posted:
December 8, 2018
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Answers (1)
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The purchasing department has analysed the number of orders placed by each of the 5 departments in the
company by type of this financial year as...
(Solved)
The purchasing department has analysed the number of orders placed by each of the 5 departments in the
company by type of this financial year as given in the table below:
An error has been found in one of these orders.
Required:
i) Determine the probability that the incorrect order was not for consumables.
ii) Determine the probability that the incorrect order came from maintenance or production.
iii) Calculate the probability that the incorrect order was an equipment order from purchase.
Date posted:
December 7, 2018
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Answers (1)
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Grear Tyre Company has just developed a new steel-belted radial tyre that will be sold through a chain of discount stores.
Because the tyre is a...
(Solved)
Grear Tyre Company has just developed a new steel-belted radial tyre that will be sold through a chain of discount stores.
Because the tyre is a new product, the company‟s management believes that the mileage guarantee offered
with the tyre will be an important factor in the consumer acceptance of product. Before finalizing the tyre mileage guarantee policy, the actual road test with the tyres shows that the mean tyre
data collected indicate that a normal distribution is a reasonable assumption.
Required:
i) Grear Tyre Company will distribute the tyres if 20 per cent of the tyres manufactured can be expected
to last more than 40,000 kilometers. Should the company distribute the tyres?
ii) The company will provide a discount on a new set of tyres if the mileage on the original tyres does not exceed the mileage stated on the guarantee.
What should the guarantee mileage be if the company wants no more than 10% of the tyres to be
eligible for the discount?
Date posted:
December 7, 2018
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Answers (1)