User Account

All Pages

Linear Programming, Advanced Statistics

Assignment Help:
1. The production manager of Koulder Refrigerators must decide how many refrigerators to produce in each of the next four months to meet demand at the lowest overall cost. There is a limited capacity in each month although this will increase in month 3. Due to a new contract, costs are expected to increase. The relevant information is provided in the table below.
Month Capacity Demand Cost of production
1 140 110 $80 per unit
2 140 150 $85 per unit
3 160 130 $90 per unit
4 160 140 $95 per unit

Each item that is left at the end of the month and carried over to the next month incurs a carrying cost equal to 10% of the unit cost in that month (e.g. anything left in inventory at the end of month one incurs an $8 cost). Management wants to have at least 30 units left at the end of month four to meet any unexpected demand at that time. A linear program has been developed to help with this. However, this may or may not be totally correct. You should verify that it is the correct formulation before solving the problem. If it is not correct, make any necessary changes to the linear program before solving it on the computer.
X1 = number of units produced in month 1; X2 = number of units produced in month 2;
X3 = number of units produced in month 3; X4 = number of units produced in month 4;
N1 = number of units left at end of month 1; N2 = number of units left at end of month 2;
N3 = number of units left at end of month 3; N4 = number of units left at end of month 4



(Continued on next page)
Minimize cost = 80X1 + 85X2 + 90X3 + 95X4 + 8N1 + 8.5N2 + 9N3 + 9.5N34
X1 < 140
X2 < 140
X3 < 160
X4 < 160
X1 = 110 + N1
X2 + N1 = 150 + N2
X3 + N2 = 130 + N3
X4 + N3 = 140 + N4
N4 > 30
All variables > 0


2. An investment advisory firm manages funds for its numerous clients. The company uses an asset allocation model that recommends the portion of each client’s portfolio to be invested in a growth stock fund, and income fund, and a money market fund. To maintain diversity in each client’s portfolio, the firm places limits on the percentage of each portfolio that may be invested in each of the three funds. General guidelines indicate that the amount invested in the growth fund must be between 20% and 40% of the total portfolio value. Similar percentages for the other two funds stipulate that between 20% and 50% of the total portfolio value must be in the income fund and at least 30% of the total portfolio value must be in the money market fund.
In addition, the company attempts to assess the risk tolerance of each client and adjust the portfolio to meet the needs of the individual investor. For example, Williams just contracted with a new client who has $300,000 to invest, and all of it must be invested. Based on an evaluation of the client’s risk tolerance, Williams assigned a maximum risk index of 0.06 for the client. The firm’s risk indicators show the risk of the growth fund at 0.10, the income fund at 0.07, and the money market fund at 0.01. An overall portfolio risk index is computed as a weighted average of the risk rating for the three funds. The average risk of the portfolio would be the total risk divided by the total investment as shown here:

(average risk) = (total risk)/(total investment).

For example, to calculate the risk of a $100,000 portfolio with 50,000 in the growth fund, 30,000 in the income fund, and 20,000 in the money market fund, the total risk would be 0.10(50,000) + 0.07(30,000) + 0.01(20,000) = 7,300; the average risk would be 7,300/100,000 = 0.073. (NOTE: When putting the risk measure into the linear program, it is better to work with the total risk rather than the average risk to avoid round-off errors.)
Additionally, Williams is currently forecasting annual yields of 8% for the growth fund, 6% for the income fund, and 2% for the money market fund. Based on the information provided, how should the new client be advised to allocate the $300,000 among the growth, income, and money market funds? A linear program has been developed to help with this. However, this may or may not be totally correct. You should verify that it is the correct formulation before solving the problem. If it is not correct, make any necessary changes to the linear program before solving it on the computer.


G = dollars invested in the growth fund
I = dollars invested in the income fund
M = dollars invested in the money market fund

Maximize yield (return) = 0.08G + 0.06I + 0.02M
Subject to:
G + I + M = 300000 Total investment
0.10G + 0.07I + 0.01M < 18000 Total risk (based on 6% average risk)
G > 60000 Minimum in growth fund
G < 120000 Maximum in growth fund
I > 60000 Minimum in income fund
I < 150000 Maximum in income fund
M > 90000 Minimum in money market fund
G, I, M > 0

NOTE: The equality for the total investment constraint simplifies the other constraints. While the total amount invested is G + I + M, this can be replaced by 300000 due to the equality condition. For example, 20% of (G + I + M) becomes 20% of $300,000 or simply $60,000. If this were a less-than-or-equal-to constraint, this could not be done and that constraint would be G > 0.20(G + I + M).

Related Discussions:- Linear Programming

Cluster analysis, Cluster analysis : A set of methods or techniques for con...

Cluster analysis : A set of methods or techniques for constructing a sensible and informative classi?cation of an initially unclassi?ed set of data, using variable values observed

Factorization theorem, The theorem relating structure of the likelihood to ...

The theorem relating structure of the likelihood to the concept of the sufficient statistic. Officially the necessary and sufficient condition which a statistic S be sufficient for

Cluster sampling, Cluster sampling : A method or technique of sampling in w...

Cluster sampling : A method or technique of sampling in which the members of the population are arranged in groups (called as 'clusters'). A number of clusters are selected at the

Integrated Economic Statistics, Advantages and disadvantages of Integrated ...

Advantages and disadvantages of Integrated Economic Statistics

Follow back surveys, Surveys which use lists related with the vital statist...

Surveys which use lists related with the vital statistics to sample individuals for the further information. For instance, the 1988 National Mortality Follow back Survey sampled de

Explain kendall''s tau statistics, Kendall's tau statistics : The measures ...

Kendall's tau statistics : The measures of the correlation between the two sets of rankings. Kendall's tau itself (τ) is the rank correlation coefficient based on number of inversi

Case-control study, Case-control study : The traditional case-control study...

Case-control study : The traditional case-control study is the common research design in the epidemiology where the exposures to risk factors for cases (individuals getting the dis

Mobile Marketing statistics., 1) Has smartphones affected the consumer beh...

1) Has smartphones affected the consumer behavior? If so How ? And how is it going to change in future? 2) Forecasting of Mobile market (Time series analysis) 3) Comparison of fou

Explanatory variables, The variables appearing on the right-hand side of eq...

The variables appearing on the right-hand side of equations defining, for instance, multiple regressions or the logistic regression, and which seek to predict or 'explain' response

Exponential order statistics model, The model which arises in the context o...

The model which arises in the context of estimating the size of the closed population where individuals within the population could be identified only during some of the observatio

Write Your Message!

Captcha
Order Assignment

Featured Services

Order Now

Popular Subjects

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

Submit Assignment

Academics

Major Subjects

Majors

Get In Touch

whatsapp: +91-977-207-8620

Phone: +91-977-207-8620

Email: [email protected]

TERMS & POLICIES

HELP & SUPPORT

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd