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

Dirichlet process mixture models, The nonparametric Bayesian inference appr...

The nonparametric Bayesian inference approach to using the finite mixture distributions for modelling data suspected of the containing distinct groups of observations; this approac

Ascertainment bias, Ascertainment bias : A feasible form of bias, particula...

Ascertainment bias : A feasible form of bias, particularly in the retrospective studies, which arises from the relationship between the exposure to the risk factor and the probabil

Expected-utility maximizer, There are two periods. You observe that Jack co...

There are two periods. You observe that Jack consumes 100 apples in period t = 0, and 120 apples in period t = 1. That is, (c 0 ; c 1 ) = (100; 120) Suppose Jack has the util

Breusch-pagan test, The Null Hypothesis - H0:  There is no heteroscedastici...

The Null Hypothesis - H0:  There is no heteroscedasticity i.e. β 1 = 0 The Alternative Hypothesis - H1:  There is heteroscedasticity i.e. β 1 0 Reject H0 if Q = ESS/2  >

Statistics, seven questions

seven questions

Non parametric maximum likelihood (npml), Non parametric maximum likelihood...

Non parametric maximum likelihood (NPML) is a likelihood approach which does not need the specification of the full parametric family for the data. Usually, the non parametric max

Describe hurdle model, Hurdle Model:  The model for count data which postul...

Hurdle Model:  The model for count data which postulates two processes, one generating the zeros in the data and one generating positive values. The binomial model decides the bina

Paired availability design, Paired availability design  is a design which c...

Paired availability design  is a design which can lessen selection bias in the situations where it is not possible to use random allocation of the subjects to treatments. The desig

Generalized method of moments (gmm), Generalized method of moments (gmm) is...

Generalized method of moments (gmm) is the estimation method popular in econometrics which generalizes the method of the moments estimator. Essentially same as what is known as the

Identifying the necessary and sufficient conditions, You have probably noti...

You have probably noticed by now that some of the statements of necessary and sufficient conditions sound more natural than others. For example it seems more natural to express "We

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