Get premium membership and access questions with answers, video lessons as well as revision papers.

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...

      

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?

  

Answers


Raphael
i) Linear programming because it usually seeks to optimize a given function subject to various
constraints. This is the case here.
copperwire2312019911i.png
copperwire2312019911ii.png
iii) Production technicians, measurement technicians, profit center personnel, cost center personnel.
The required parameters will be reaction times, profit information, cost information and timing
information.
raphael answered the question on January 23, 2019 at 18:13


Next: Explain and graphically show the following terms as used in linear programming: i) Alternate optimal or multiple solutions ii) Unbound solutions iii) Infeasible solutions
Previous: Briefly and clearly compare and contrast between a transportation problem and an assignment problem as used in linear programming.

View More CPA Quantitative Analysis Questions and Answers | Return to Questions Index


Learn High School English on YouTube

Related Questions


  • 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:
    kenyacanning1412019949.png
    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
    extract1412019945.png
    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:
    tamutamu1412019930.png
    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
    regal1112019924.png
    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.
    endowment1112019.png
    endowment1112019b.png

    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.
    pension1112018859.png
    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:
    simplex1112019759.png
    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:
    manji1112029752.png
    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)
    movingaverage1112019.png

    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:
    ite1012019.png
    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:
    kgs10102019.png
    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?
    kgs10102019b.png

    Date posted: January 10, 2019.  Answers (1)