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i) A linear program is one that optimises a linear objective function with given decision variables
subject to conditions that the constraints are linear and the variables are non-negative.
ii) The basic feasible solution is the set of variable values at a corner point of the feasible region (set of values for decision variables that satisfy both non-negativity and the structural constraints)
iii) Degeneracy is a case where one or more basic variables have values of zero in the optimal solution.
iv) Alternate optimal solution is said to exist when the number of optimal solutions is infinite and a
given constraints is binding (further improvement on objective function is prohibited)
v) Redundant constraint is one that has no effect on the solution space. It contributes nothing to the
solution space.
vi) Range of optimality represents the limits for which a solution remains optimal
vii) Artificial variable is one that is added to the LHS of starting basis so as to preclude yielding of
infeasible (negative) solution for a mixed constraint situation.
viii) Reduced cost represents the reduction in profit due to addition of a non-limiting resource
ix) Dummy destination is one that is introduced so as to take care of excess supply. It has zero profit
or cost.
x) Assignment problem is a special kind of problem where there are a number of supplies to satisfy
equal number of destinations
Mutiso answered the question on January 14, 2019 at 18:48
- 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)
- 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. Answers (1)
- 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. Answers (1)
- 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. Answers (1)
- 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. Answers (1)
- As a tax consultant to the Government of your country, you have been asked to estimate an empirical
model on the demand for income tax evasion...(Solved)
As a tax consultant to the Government of your country, you have been asked to estimate an empirical
model on the demand for income tax evasion (ITE) in the country. You think true income (TI),
Marginal tax rate (MTR), penalty rate (PR) and probability of detection (PROB) will be important
variables. Using national time-series annual data from 1967 to 1995, you estimate the following
regression equation:
The calculated t – statistics are reported in parentheses, and figures are in shillings.
Required:
i) Write down the population theoretical empirical model on the demand for income tax evasion
(ITE).
ii) Provide a theoretical justification of the empirical model specification in (i) above, that is, expected
signs of the regression coefficients and why.
iii) Interpret the constant term (-52.59), coefficient for true income (33.44) and coefficient of
probability of detection (-1.48) in the context of the problem.
iv) Before collecting data, the principal tax collector and her staff believed that penalty rate had a
negative influence on income tax evasion and should therefore be used as leverage on those who
evade tax.
From the regression results, should this be the case? Why?
(Note: critical t-value = - 1.701 at 0.05 level of significance)
Date posted: January 10, 2019. Answers (1)
- Briefly but clearly, explain the difference, if any, between regression analysis and correlation analysis.(Solved)
Briefly but clearly, explain the difference, if any, between regression analysis and correlation analysis.
Date posted: January 10, 2019. Answers (1)
- Kenya Graduate School (KGS) offers a variety of graduate courses. However, its main emphasis has been on
information science (IS) courses. Due to the laboratory equipment...(Solved)
Kenya Graduate School (KGS) offers a variety of graduate courses. However, its main emphasis has been on
information science (IS) courses. Due to the laboratory equipment requirements for IS courses, KGS has to
estimate in advance the expected students enrolments. Over the last 5 years, the students enrolments, by
quarter, has been:
Required:
a) Determine the estimates, by quarter, for year 1996. Justify the method you use.
b) If linear multiple regression were to be used in order to determine the predicting equation, what other
variables would be included?
c) How would the expected enrolments be compared to the actual enrolments?
Date posted: January 10, 2019. Answers (1)
- In recent years environmentalists and health professionals have been concerned about the ill effects onthe environment of the widespread use of insecticides. If human beings...(Solved)
In recent years environmentalists and health professionals have been concerned about the ill effects on
the environment of the widespread use of insecticides. If human beings are to cope with the problem
and make decisions about how to deal with it, they must understand the effect of insecticides on humans
and other animals. In the kind of study often done to promote such understanding, two professors at
University of Nairobi investigated the effect of a commonly used insecticide on sheep. Among other
statistical analyses, they derived the following linear regression equation (n = 16):
This equation describes the relationship between the activity of a certain enzyme in the
sheep's brain (Y)and the time (in hours) after the sheep has been exposed to the insecticide (X).
Required:
i) Suppose 30 hours have elapsed since a sheep has been exposed to the insecticide, what is the
predicted value of Y?
ii) How would you describe the relationship between the two variables?
iii) The professors computed a coefficient of determination (r2) of 0.86 from the data. What
conclusion can be drawn about the true relationship between the two variables?
iv) What assumption are necessary to solve part (iii) above?
Date posted: January 1, 2019. Answers (1)
- Does a high correlation mean that one variable causes another variable to vary?(Solved)
Does a high correlation mean that one variable causes another variable to vary?
Date posted: January 1, 2019. Answers (1)
- Does finding a no linear relationship between two variables mean no relationship?(Solved)
Does finding a no linear relationship between two variables mean no relationship?
Date posted: January 1, 2019. Answers (1)