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# Optimization

### Optimization : Comparing two probability distributions.

F and G are cumulative probability distributions with identical support. G first order stochastically dominates F, i.e., for every X on the support, F(x) > G(x). Prove (or disprove) the proposition that argmax [X(1-G(X))] > argmax [X(1-F(X))], where argmax is the value of x that maximizes the expression in brackets. See atta

### Dynamic Programming Problem

A company is planning its advertising strategy for next year for its three major products. Since the three products are quite different, each advertising effort will focus on a single product. In units of millions of dollars, a total of 6 is available for advertising next year, where the advertising expenditure for each product

### Quantitative Methods

39. Max Z = \$0.30x + \$0.90y Subject to : 2x + 3.2y 160 4x + 2y 240 y 40 x, y Solve for the quantities of x and y which will maximize Z. What is the value of the slack variable associated with constraint 2? 40. The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Tw

### Operations Problems

3.The costs to transport goods between outlets is listed below. What is the minimum cost and associated routing to ship from A to B and E on the same delivery run? A B C D E A 0 3 4 7 11 B 3 0 6 4 13 C 4 6 0 5 8 D 7 4 5 0 9 E 11 13 8 9 0 4. Four assembly plants can produce Tyco tricycles. The production capacitie

### Optimization and Minimizing Cost

A factory wants the power company to run a special line to the plant. The power company is located 1000 meters down a river on the opposite bank. Ground lines cost \$20 per meter. The river is 500 meters wide and underwater line will cost M (M> 1) times as much per meter as the above ground line. Since the factory owns the riverf

### What is the project's duration if only normal times are used?

Information concerning a project is given below. Indirect project costs amount to \$250 per day. The company will incur a \$100 per day penalty for each day the project lasts beyond day 14. a) What is the project's duration if only normal times are used? b) What is the minimum-cost schedule? c) What is the critical path for the

### Evaluating the Maximum and Minimum Values of a Function

Find the maximum and minimum values of the function f (x,y, z) = x + 2y subject to the constraints y^2 + z^2 = 144 and x + y + z = 4. Maximum value is ____, occurring at (____, ____, ____). Minimum value is ____, occurring at (____, ____, ____).

### Find the max and min values

Find the max and min values of f(x,y) = 6x+y on the ellipse x^2 + 4y^2 = 1

### Maximum and Minimum of the Function

Find the absolute maximum and minimum of the function f(x, y, z) = yz + xy subject to the constraints y^2 + z^2 and xy = 6. See attached file for full problem description.

### Question about Maximum and minimum volumes of a rectangular box

Find the maximum and minimum volumes of a rectangular box whose surface area equals 8000 square cm and whose edge length (sum of lengths of all edges) is 480 cm. See attached file for full problem description.

### Solve the following problem for the optimal number of clerks:

There are approximately 300 customers shopping in Fackert Department Store in Mexico City between 9 a.m. and 5 p.m. on Saturdays. When deciding how many cash registers to keep open each Saturday, owner Susanna Fackert considers 2 factors: customer waiting time (and the associated waiting cost) and the service costs of employing

### Managerial Finance - questions/problem about General Electric Corporation and Tyco International

A. The following is the scenario you should consider when answering: General Electric Corporation and Tyco International are both classified as "conglomerates" (having many diversified business lines). General Electric has pursued a conservative growth strategy by focusing on being the number one or number two in each indu

### Lagrange Multiplier Optimization

Please explain the two constrained optimization problems using a lagrangian multiplier. Problem one as follows: Maxamize f(x,y)= x ^1/3 y^2/3 subject to x+2y=100 The next one is a three variable problem max f(x,y,z)=x ^ 1/4 y ^ 2/4 z ^ 1/4 subject to 2x+2y+2z = 100 I understand how to set the problem up with parti

### Finance : Income, Cash Flow, Balance Sheets, Forecasting and Sustainable Growth

2. During 1998, the Senbet Discount Tire Company had gross sales of \$1 million. The frim's cost of googs sold and selling expenses were \$300,000 and \$200,000, respectively. These figures do not include depreciation. Senbelt also had notes payable of \$1 million. These notes carried an interest rate of 10 percent. Depreciation was

### Linear Programming : Optimization and Maximization

Joe has \$250,000 to invest. He is considering four options" Bonds Fund Exxon MicroSoft Real Estate Fund Price per share \$50 \$100 \$80 \$40 Annual Rate of Return 0.06 0.12 0.08 0.09 Risk measure per \$ invested 0.05 0.10 0.08 0.11 Joe wants at least a 9% annual rate of return No one stock can be mor

### Constrained Optimization Problems

Solve the following constrained optimization problems: a) max x1,x2 x1^2 +x2^2 subject to.... b)..... Please see the attached file for the fully formatted problems.

### Finding Maximum Profit

Let P(x) = 28x -x^2 be the profit from the manufacture and sale of x toys. What production level maximizes profit?

### Finding the relative maximum point of function.

Find the relative maximum point for the function f(x) = -x^3 + 3x^2 +24x +5

### Optimization problem

Here is the word problem: A mass of clay of volume 432in^3 is formed into two cubes. What is the minimum possible total surface area of the two cubes? What is the maximum? I have determined the following: Surface Area (SA) = 6a^2 Volume of a cube (V) = a^3 I am not sure how to setup the formula to determine the asked fo

### Optimization for Genetic Algorithms

This is reserve for a Specific OTA you can solve the problem using genetic algorithm(GA),but do you think you can get near the solution in the the "Result_2_Xugang" PDF file i sent.please describe why this algorithm good fro my case. I NEED THE WHOLE CODES PLEASEEEEEEEEEEEEEE. some test data is needed to see the benefi

### Optimization Algorithm : Prony Series

1 Definition of a Prony Series Let GR(t) be the shear stress relaxation modulus. Define G1 and G0 by the following limits: ... From the shear relaxation modulus we can define a dimensionless relaxation modulus from: .... The normalized shear stress relaxation modulus is often represented by a series expansion in exponential

### Optimization algorithm

Could you solve the following approach "in the 2nd page of the PDF file" using matlab. Let me know if you are interesting to solve this problem.i can pay anything you want.there is an Optimization involve in step #5 "you can use any Optimization method you know to solve it.I prefer the two-phase global optimization algorithm. i

### If he uses the maximax criterion, which size bus will he purchase? If he uses the maximin criteria, which size bus would he purchase? If he uses Bayes' decision rule, which size bus would he purchase? What is the expected annual profit for the bus that he will decide to purchase using Bayes' decision rule?

The operations manager for a community bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in \$000) will vary depending upon whether passenger demand is low, medium, or high as follows: Bus Low Medium High Small

### Recursive definitions

(See attached file for full problem description) --- Give a recursive definition of a) of the functions max and min so that mx{a1,a2,..an and min {a1,a2,...an} are the maximum and minimum of the n numbers a1,a2,...an respectively b) prove that f12+f22+..fn2 = fnfn+1 whenever n is a positive integer fn is the Fibonacci sequ

### Quantitative Methods: Forecasting, Trends and Mean Square Error

Month 1993 January 1.45 February 1.80 March 2.03 April 1.99 May 2.32 June 2.20 July 2.13 August 2.43 September 1.90 October 2.13 November 2.56 December 4.16 Using the chart above I need to: a. Forecast the month of December using a moving average of 3. b. Calculate the Mean-Square Error (MSE).

### Operations research

Photo-Max, a large photographic outlet, receives 5,000 collapsible tripods annually from Quality Photographic Suppliers to meet annual demand. The ordering cost is \$15 per order, and the carrying cost is \$0.50 per unit per year. Quality Photographic, building on its established reputation for on-time delivery, is interested in s

### Forecasting with seasonal component

Quarterly billing for water usage is shown below. Yr. 1 Yr. 2 Yr. 3 Yr.4 Winter 64 66 68 73 Spring 103 103 104 120 Summer 152 160 162 176 Fall 73 72 78 88 Use the information abov

### Forecasting

Explain what makes quantitative forecasting methods appropriate.

### Linear Programming : Optimal Solutions

Ace Lumber and Building Supply in Andover, Maryland, has received the following order for standard 1x12 boards to be cut in three lengths Order for 1x12 Boards Length Quantity 7 ft 700 9 ft 1200 10 ft 300 The company maintains 1x12 boards in 25-foot standard-length in stock. Therefore,

### Wave Equation: Finite String and Maximum Displacement

Q Ut4iOE) 3 A finite string of length L that is fixed at both ends and is released from rest with an initial displacement will have the following mathamatical description by the wave equation U =a^2 Uxx Given a = 30 m/s and the initial velocity of 300sin(4 pi x) from Its equilibrium position and L = 4m. find the solution for