Login

Create Account
+14156709189
info@expertsmind.com
Submit Homework/Assignment
Get quote & make Payment
Get Solution
Linear Programming, Advanced Statistics
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 roundoff 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 lessthanorequalto constraint, this could not be done and that constraint would be G > 0.20(G + I + M).
Posted Date: 4/3/2013 10:50:06 PM  Location :
Ask an Expert
Related Discussions:
Linear Programming, Assignment Help, Ask Question on Linear Programming, Get Answer, Expert's Help, Linear Programming Discussions
Write discussion on Linear Programming
Your posts are moderated
Write your message here..
Related Questions
Explain regression through the origin, Regression through the origin : In s...
Regression through the origin : In some of the situations a relationship between the two variables estimated by the regression analysis is expected to pass by the origin because th
Generalized additive model, The linear component ηi, de?ned just in the tra...
The linear component ηi, de?ned just in the traditional way: η i = x' 1 A monotone differentiable link function g that describes how E(Yi) = µi is related to the linear compon
Dropout, A subject who withdraws from the study for whatever reason, advers...
A subject who withdraws from the study for whatever reason, adverse side effects, noncompliance, moving away from the district, etc. In number of cases the reason may not be known.
Calculate the probability, (a) A plane timetable states that a particular p...
(a) A plane timetable states that a particular plane is due at 2pm but the actual arrival time isuniformly distributed between 1pm and 3pm. (i) Calculate the probability that th
Reliability theory, Reliability theory is the theory which attempts to det...
Reliability theory is the theory which attempts to determine the reliability of the complex system from knowledge of the reliabilities of the components. Interest might centre on
Frequency polygon, It is the diagram used to display the values graphically...
It is the diagram used to display the values graphically in a frequency distribution. The frequencies are graphed as an ordinate against the class midpoints as abscissae. The p
Non central distributions, Non central distributions is the series of prob...
Non central distributions is the series of probability distributions each of which is the adaptation of one of the standard sampling distributions like the chisquared distributio
Draw histogram of income, The skewness is a measure of asymmetry and as it ...
The skewness is a measure of asymmetry and as it is positive at 4.29, it is greater than zero which reveals that the tail extends to the right indicating the distribution to be mor
Business forcastin.., elements , importance, limitation, and theories
elements , importance, limitation, and theories
Population averaged models, Population averaged models are the models for ...
Population averaged models are the models for kind of clustered data in which the marginal expectation of response variable is the main focus of interest. An alternative approach
Assignment Help
Accounting Assignment Help
Economics Assignment Help
Finance Assignment Help
Statistics Assignment Help
Physics Assignment Help
Chemistry Assignment Help
Math Assignment Help
Biology Assignment Help
English Assignment Help
Management Assignment Help
Engineering Assignment Help
Programming Assignment Help
Computer Science Assignment Help
IT Courses and Help
ExpertsMind Services
Online Tutoring
Projects Assistance
Exam Preparation
Coursework Help
Programming Courses
Engineering Courses
Why Us ?
~Experienced Tutors
~24x7 hrs Support
~Plagiarism Free
~Quality of Work
~Time on Delivery
~Privacy of Work