Login

Create Account
Customer Service Chat
+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
Describe lengthbiased sampling, Lengthbiased sampling : The bias which ar...
Lengthbiased sampling : The bias which arises in the sampling scheme based on the visits of patient, when some individuals are more likely to be chosen than others simply because
Banach''s matchbox problem, Banach's matchbox problem : The person carrie...
Banach's matchbox problem : The person carries two boxes of matches, one in his left and one in his right pocket. At first they comprise N number of matches each. When the person
Cauchy distribution, Cauchy distribution : The probability distribution, f ...
Cauchy distribution : The probability distribution, f (x), can be given as follows where α is the position of the parameter (median) and the beta β a scale parameter. Moments
Calibration, Calibration : A procedure which enables a series of simply obt...
Calibration : A procedure which enables a series of simply obtainable but inaccurate measurements of some quantity of interest to be used to provide more precise estimates of the r
Explain interim analyses, Interim analyses : An analysis made before the pl...
Interim analyses : An analysis made before the planned end of a clinical trial, typically with the aim of detecting the treatment differences at the early stage and thus preventing
Ehrenberg''s equation, The equation linking the height and weight of the ch...
The equation linking the height and weight of the children between the ages of 5 and 13 and given as follows here w is the mean weight in kilograms and h the mean height in
To create a relative frequency histogram, The total amount of protein produ...
The total amount of protein produced by a dairy cow can be estimated from periodic testing of her milk. The following are the total annual protein production values (lb) for 28 tw
Experimental design, i have an assignment for experimental design which is ...
i have an assignment for experimental design which is must done by SAS program can you help me also i need to hand in the assignment till thursday shall i send it for you ?
Hypothesis testing, t distribution
t distribution
Deviance, The measure of the degree to which the particular model differs f...
The measure of the degree to which the particular model differs from the saturated model for the data set. Explicitly in terms of the likelihoods of the two models can be defined a
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
ExpertsMind Services
Online Tutoring
Projects Assistance
Exam Preparation
Coursework Help
Programming Help
IT Services
Why Us ?
~Experienced Tutors
~24x7 hrs Support
~Plagiarism Free
~Quality of Work
~Time on Delivery
~Privacy of Work