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a) Decision making under risk is when decisions are made using already known probabilities for states of
nature or outcomes. The probabilities can come from previous data.
Decision making under certainty is when a decision is made where there is no prior probabilities for
states of nature or outcomes.
b) Decision tree is a diagrammatic representation of decisions given different states of nature. Nodes and branches are used to represent the decisions and outcomes from given decisions.
Probability tree is a diagrammatic representation of the sequence of outcomes given certain probabilities.
c) Minimax criterion-involves choosing the alternative with minimum regret from choice of maximum
regrets from given events.
Maximax criterion- involves choosing the alternative with maximum payoff from choice of maximum
payoffs from given events.
d) Pure strategy in a game is where each player knows exactly what the other player is going to do. The
same rule is still followed each time.
Mixed strategy is where there is a combination of the rules followed. Each player does not know what
the other player is going to do. In this case probabilities are used to find what each player will do. The main aim is to maximize expected gains or to minimize losses.
e) Games represent a competitive situation where players aim to gain from each other.
Games with more than two persons represent real life situation where there are more than two persons
as players. Each person seeks to gain from the others.
Non-zero sum games represent situation where it is not necessarily that what one losses is gained by
another.
Mutiso answered the question on January 23, 2019 at 20:51
- 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. Answers (1)
- 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. Answers (1)
- 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. Answers (1)
- 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. Answers (1)
- Downtown Motors Company (DMC), has hired a market services firm to develop an advertising strategy
for promoting Downtown?s used car sales. The marketing firm has recommended...(Solved)
Downtown Motors Company (DMC), has hired a market services firm to develop an advertising strategy
for promoting Downtown's used car sales. The marketing firm has recommended that
Downtown uses pot announcements on both television and radio as the advertising media for the
proposed promotional campaign. Advertising strategy guidelines are expressed as follows:
1. Use at least 30 announcements for combined television and radio coverage.
2. Do not use more than 25 radio announcements.
3. The number of radio announcements cannot be less than the number of television announcements. The
television station has quoted a cost of Sh.1,200 per spot announcement and the radio station has quoted a
cost of Sh.300 per spot announcement. Downtown‟s advertising budget has been set at
Sh.25,500. The marketing services firm has rated the various advertising media in terms of audience
coverage and recall power of the advertisement. For Downtown‟s media alternatives, the
television announcement is rated at 600 and the radio announcement is rated at 200.
Required:
Perform an analysis of advertising strategy for DMC. Include a consideration of the following items:
i) Determine the optimal number of television and radio spot announcements.
ii) Explain the relative merits of each advertising medium.
iii) Determine the rating that would be necessary in order to increase the number of television spots.
iv) Which restrictions placed on the advertising strategy would DMC want to consider relaxing or
altering? Why?
v) What is the use of any possible increase in the advertising budget?
Date posted: January 23, 2019. Answers (1)
- Briefly and clearly compare and contrast between a transportation problem and an assignment problem
as used in linear programming.(Solved)
Briefly and clearly compare and contrast between a transportation problem and an assignment problem
as used in linear programming.
Date posted: January 23, 2019. Answers (1)
- The Copper Wire Company is a manufacturer of copper wires. Ben Muturi, the company executive
director has just received a memo from Stella Musingo, one of...(Solved)
The Copper Wire Company is a manufacturer of copper wires. Ben Muturi, the company executive
director has just received a memo from Stella Musingo, one of his young engineers. Stella informs Ben
that; with the forthcoming purchase of new blast furnace to produce copper, it seems an opportune time
to completely review their method of producing copper. Currently, a variety of ingredients are entered
into the blast furnace in order to produce copper. The production manager, Joe Kiilu makes the
decision, as he has for the last 25 years, on the variety of ingredients. It is not an easy decision. The company wants to keep the costs of producing copper down
The ingredients into the blast furnace have to interact to produce copper. Furthermore, the chemical
reactions have to be such that the copper produced is viscous enough to flow out of the furnace.
Stella has identified the problems with the current method. First, Joe is retiring in six months and there
is no obvious replacement to him. Second, the company never knows if they are minimizing the
production costs. Third, sometimes the furnace does not freeze-up. Stella believes that there is a
quantitative technique, which can be used to decide what ingredients to enter in to the furnace. Once the model has been developed, special skills such as Joe‟s will no longer be required. The
company will also be confident that they are minimizing costs. In addition, they would be able to
eliminate the furnace freeze-up problem
Required:
i) What potential quantitative technique can be used to solve this problem? Why?
ii) Specify the general formulation of the quantitative technique. (Be sure to clearly spell out the
meaning of all the variables or parameters used)
iii) If a group were formed to develop an appropriate model, what organizational personnel should be
included? What specific skills would each provide?
Date posted: January 23, 2019. Answers (1)
- Explain and graphically show the following terms as used in linear programming:
i) Alternate optimal or multiple solutions
ii) Unbound solutions
iii) Infeasible solutions(Solved)
Explain and graphically show the following terms as used in linear programming:
i) Alternate optimal or multiple solutions
ii) Unbound solutions
iii) Infeasible solutions
Date posted: January 23, 2019. Answers (1)
- 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. Answers (1)
- Explain the following terms as used in the context of linear programming:
i) Linear program
ii) Basic feasible solution
iii) Degeneracy
iv) Alternative optimal solutions
v) Redundant constraints
vi) Range of...(Solved)
Explain the following terms as used in the context of linear programming:
i) Linear program
ii) Basic feasible solution
iii) Degeneracy
iv) Alternative optimal solutions
v) Redundant constraints
vi) Range of optimality
vii) Artificial variables
viii) Reduced cost
ix) Dummy destination
x) Assignment problem
Date posted: January 14, 2019. Answers (1)
- An extract of the output from a computer package for this problem is given below:
Output solution(Solved)
An extract of the output from a computer package for this problem is given below:
Output solution
Required:
i) Interpret the output clearly, including optimum product mix, monthly profit, unused resources and
dual values
ii) Explain the purpose of upper limits and lower limits for the variables X1,X2,X3 and constraints 1 to
5.
iii) Calculate the increase in profit if the company is able to produce a further 10 CPU 80386 chips.
Date posted: January 14, 2019. Answers (1)
- J.A Computers is a small manufacturer of personal computers. It concentrates on production of three
models- a Desktop 386, a Desktop 286, and a Laptop 486,...(Solved)
J.A Computers is a small manufacturer of personal computers. It concentrates on production of three
models- a Desktop 386, a Desktop 286, and a Laptop 486, each containing one CPU Chip. Due to its
limited assembly facilities JA Computers are unable to produce more than 500 desktop models or more
than 250 Laptop models per month. It has one hundred and twenty 80386 chips (these are used in
Desktop-386) and four hundred 80286 chips (used in desktop 286 and Laptop 486) for the month. The Desktop 386 model requires five hours of production time, the Desktop 286 model requires four hours
of production time, and the Laptop 486 requires three hours of production time. J.A Computers have
2000 hours of production time available for the coming month. The company estimates that the profit
on Desktop 386 is Sh. 5,000. for a desktop 286 the profit is Sh.3,400 and Sh.3,000 profit for a laptop
486.
Required:
Formulate this problem as a profit maximization problem and mention the basic assumptions that are
inherent in such models.
Date posted: January 14, 2019. Answers (1)
- Explain the value of sensitivity analysis in linear programming problems and show how dual values are
useful in identifying the price worth paying to relax constraints.(Solved)
Explain the value of sensitivity analysis in linear programming problems and show how dual values are
useful in identifying the price worth paying to relax constraints.
Date posted: January 14, 2019. Answers (1)
- 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. Answers (1)
- Define the following terms as used in linear programming:
i) Feasible solution
ii) Transportation problem
iii) Assignment problem(Solved)
Define the following terms as used in linear programming:
i) Feasible solution
ii) Transportation problem
iii) Assignment problem
Date posted: January 14, 2019. Answers (1)
- a) A small company will be introducing a new line of lightweight bicycle frames to be made from special
aluminium alloy and steel alloy. The frames...(Solved)
a) A small company will be introducing a new line of lightweight bicycle frames to be made from special
aluminium alloy and steel alloy. The frames will be produced in two models, deluxe and professional.
The anticipated unit profits are currently Sh.1,000 for a deluxe frame and Sh.1,500 for a professional
frame. The number of kilogrammes of each alloy needed per frame is summarized in the table below. A
supplier delivers 100 kilogrammes of the aluminium alloy and 80 kilogrammes of the steel alloy weekly.
-------------Aluminium alloy---Steel alloy
Deluxe--------2----------------3
Professional--4----------------2
Required:
i) Determine the optimal weekly production schedule.
ii) Within what limits must the unit profits lie for each of the frames for this solution to remain
optimal?
b) Explain the limitations of the technique you have used to solve part (a) above.
Date posted: January 11, 2019. Answers (1)
- 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. Answers (1)
- Regal Investments has just received instructions from a client to invest in two shares; one an airline share, the other an insurance share. The total...(Solved)
Regal Investments has just received instructions from a client to invest in two shares; one an airline share, the other an insurance share. The total maximum appreciation in share value over the next year is to be maximized subject to the following restrictions:
- the total investment shall not exceed Sh.100,000
- at most Sh.40,000 is to be invested in the insurance shares
- quarterly dividends must total at least Sh.2,600
The airline share is currently selling for Sh.40 per share and its quarterly dividend is Sh.1 per share. The insurance share is currently selling for Sh.50 per share and the quarterly dividend is Sh.1.50 per
share. Regal's analysts predict that over the next year, the value of the airline share will increase by Sh.2 per share and the value of the insurance share will increase by Sh.3 per share.
A computer software provided the following part solution output:
Objective Function Value = 5,400
Required:
a) Formulate the above problem.
b) Explain what reduced cost and dual prices columns above mean.
c) How should the client‟s money be invested to satisfy the restrictions?
d) Suppose Regal‟s estimate of the airline shares appreciation is an error, within what limits
must the actual appreciation lie for the answer in (c) above to remain optimal?
Date posted: January 11, 2019. Answers (1)
- An endowment fund manager is attempting to determine a “best” investment portfolio and is considering six
alternative investments. The following table indicates point estimates for the...(Solved)
An endowment fund manager is attempting to determine a “best” investment portfolio and is considering six
alternative investments. The following table indicates point estimates for the price per share, the annual
growth rate in the price per share, the annual dividend per share, and a measure of the risk associated with each investment.
Date posted: January 11, 2019. Answers (1)
- A pension fund wishes to invest in one or more of six possible investments. Financial analysts have estimated the present value of effective annual estimate....(Solved)
A pension fund wishes to invest in one or more of six possible investments. Financial analysts have estimated the present value of effective annual estimate. The data in this table indicate that the present value of investing USD 10,000 in alternative 1 is the sum of USD 1,200 (0.12 x USD 10,000) for year 1, USD 1,000 (0.10 x 10,000) for year 2, and USD 800 (0.08 x USD 10,0000 for year 3, for a total present value of USD 3,000.
Management has decided that USD300,000 will be invested. At least USD50,000 is to be invested in alternative 2 and no more than USD40,000 in alternative 5. Total investment in alternative 4 and 6 should not exceed USD75,000, as these are risky investments.
If the objective is to maximize the present value of total dollar return for the three-year period, formulate the LP model for how much capital to invest in each alternative.
Can you comment on how relevant each underlying LP assumption is to this problem?
Date posted: January 11, 2019. Answers (1)