Explore BrainMass

# Optimization

### Trends and Forecasting : Writing and Using Difference Equations

1. Consider a savings account started with an initial deposit of y(0) dollars. The interest rate is r percent per annum and the interest is compounded every month. The depositor is allowed to make additional deposits every month, say, u(1), u(2), u(3), and so on. Write a difference equation that will model the balance at the end

### Complex : Maximum and Minimum Moduli

Find the maximum and the minimum moduli of the function on the set . (Upper half of the closed unit disc around the origin). Find all points where these maximum and minimum are attained. Please see the attached file for the fully formatted problems.

### Functions : Intervals of Concavity, Inflection Points, Critical Points, Maxima, Minima (Extrema) (5 Problems)

Please see the attached file for the fully formatted problems.

### Maximum and Minimum theorem

Prove: A continuous mapping T of a compact subset M of a metric space X into assumes a maximum and a minimum at some points of M.

### Finding the maximum value of a function subject to constraint satisfaction.

The maximum value of z = 20x + 8y subject to 3x + y < 24 6x + 4y < 66 x > 0, y > 0 is: A. 220 B. 160 C. 172 D. 132

### Find maximum value of sin(x) + 3cos(x)

Find maximum value of sin(x) + 3cos(x)

### Optimization

If a company has m hours of machine time and w hours of labor, it can produce 3m^(1/3)w^(2/3) units of a product. Currently, the company has 216 hours of machine time and 1,000 hours of labor. An extra hour of machine time costs \$100, and an extra hour of labor costs \$50. If the company has \$100 to invest in purchasing addition

### Fire department staffing schedule optimization

A fire dept. says that they must have full time firemen work on different days of the week. they must have 10 on mon, 11 on tues, 12 on wed, 13 on thurs, 14 on fri, 15 on sat and 16 on sun . each fireman must work 5 (any 5) consecutive days and then have two days off. but sometimes they can work one day a week OT. each fireman i

### A fire department says that they must have full time firemen work on different days of the week.

A fire department says that they must have full time firemen work on different days of the week. They must have 10 on mon, 11 on tues, 12 on wed, 13 on thurs, 14 on fri, 15 on sat and 16 on sun. Each fireman must work 5 (any 5) consecutive days and then have two days off. but sometimes they can work one day a week OT. each firem

### Transportation, Transshipment, and Assignment Problems: Supply, Demand and Optimal Solution

A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation cost are: Destination Assembly Plant 1 2 3 Supply Source A 5 9 16 200 Factory B 1 2 6 400 C 2 8 7 200 Demand 120 620 60 What are the t

### Transportation, Transshipment, and Assignment Problem

I need help trying to find the answer. I have tried about 20 different constraints and all of them are wrong. I don't know what I am doing wrong. Some of the constraints that I have tried are x4 + x6 = 175 and x6 + 0 = 175 just to give you an idea of the way that I am thinking. Evidently it is wrong. Please guide me in the

### Determining Maximum Profit

Sue and Joan are making cloth pins for a craft show. They have enough fabric to make at most 40 giraffe pins and 80 frogs. They know they will be able to sell at least 20 giraffes and 60 frogs. However, they have time to make only a total of 110 pins. If their is \$4.90 for each giraffe and \$1.25 for each frog, what is their maxi

### Functions : Maximum and Minimum Values, Subject to Constraints

Find the maximum and minimum values of this function: G= 7X+16y subject to 7x+3y is less than or greater to 37 x is greater than or equal to 0 y is greater than or equal to 0

### Find critical numbers, inflection points, absolute max and absolute min values for the following given functions:

Find critical numbers, inflection points, absolute max and absolute min values for the following functions: (a) f(x) = sqrt(x^2-8x+32) * (x-4) (b) f(x) = x*sqrt(x^2+4)

### Forcasting Models and Multiple Regression

Study Question dealing with forcasting models using mutiple regression, holts method, simple exponential smoothing, and the winters method to make predictions. (See attached file for full problem description) --- a. Use this data and multiple regression to make predictions for the motel chain's sales during the next 4 qua

### Optimization

Specify whether the following statements are true or false and justify your answer. a) Suppose we have an optimal basic feasible solution for an LP in standard form. If we increase the cost of a non-basic variable xn, the current solution will always remain optimal. b) Suppose we have an optimal basic feasible solution for

### Optimization for fencing a storage yard

The management of a large store has 800 feet of fencing to fence in a rectangular storage yard using the building as one side of the yard. If fencing is used for the remaining sides, find the area of the largest possible yard. A long sheet of metal, one foot wide(12 inc) is to be turned up at both sides to make a horizontal g

### Optimization Problems/ Newtons Method

--- 4) Find a positive number such that the sum of the number and its reciprocal is as small as possible 6) Find the dimensions of a rectangle with area 1000m^2 whose perimeter is as small as possible 10) A box with square base and open top must have a volume of 32,000cm^3. Find the dimensions of the box that minimize

### Max/min/crit point values

(See attached file for full problem description) --- 1) Let F(x) = 2âˆšX - X A. Find the local maximum and minimum values of F (x) in the interval [0,9] B. Determine whether F(x) satisfies al the conditions of MVT in the interval [0,9]. If f(x) satisfies the condition of MVT determine the 'c' value that satisfies the co

### Network Flow Models; Supply, Demand, and Transshipment Nodes; Optimization in Excel; Solver

Problem: A furniture manufacturer has warehouses in cities represented by nodes 1, 2, and 3 in Figures 5.34. The values on the arcs indicate the per unit shipping costs required to transport living room suites at each warehouse is indicated by the negative number next to nodes 1, 2, and 3. The demand for living room suites is

### Linear Programming : Algabraic Formulation and Spreadsheet Modeling using Excel and Solver

Optimization Problem using Excel add-in Solver This problem requires the use of Excel and the add-in, called Solver. The course is Excel-based and Solver is the optimization application used for all problems. The problem appears in this text box and is also attached as a MS Word file, so it is sure to transmit legibl

### Optimization Problem using Excel add-in Solver

This problem requires the use of Excel and the add-in, called Solver. The course is Excel-based and Solver is the optimization application used for all problems. This particular problem comes from Cliff Ragsdales's " Spreadsheet Modeling and Decisoin Analysis" and is case problem 6.3. The problem appears in this text box an

### Duality in piecewise linear convex optimization

(See attached file for full problem description) Hint: Consider the linear program: Min v St. Ax-ve <= b Where X is in Rn and v is in R

### Optimization, Derivatives, Quadratic Equations - The value of good wine increases with age

The value of good wine increases with age. Thus if you are a wine dealer, you have the problem of deciding whether to sell you wine now, at a price of \$P a bottle, or sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of wine t years from now is \$P(1+20(sqr(t))). Assu

### Solve for X and Finding a Value of b that Maximizes a Function.

A. Solve X2 +X + 1 - &#8730;(X2 + 3X + 1) = 8 b. Find b such that f(X) = -4X2 + bx +3 the maximum value of 50.

### Transportation Problem : Find Optimal Solution

Find the optimal solution for the following problem: TO FROM Chicago Atlanta supply St louis 40 63 250 Richmond 70 30 400 demand 300 350 650

### Rootfinding and Optimization : Newton's, Secant, Bisection, False Position Methods

3. (Rootfinding and Optimization) (a) Suppose that f is differentiable on [a, b]. Discuss how you might use a rootfinding method to identify a local extremum of f inside [a, b]. (b) Let f(x) = logx ? cosx. Prove that f has a unique maximum in the interval [3,4]. (NB: log means natural logarithm.) (c) Approximate this local ma

### Proof of Dual using Farkas Lemma (PhD)

Hello, Could you please help me to prove this using Farkas Lemma? Well, I initially thought that I can use Farkas Lemma, but if it is impossible to use the lemma (though I do belive it will help), you might try other way. Thank you! --- (See attached file for full problem description)

### Find the relative maxima and minima

Find the relative maxima and minima of f(x)=x^4-8x^3+22x^2-24x+20.

### Drug Concentration : Finding Time of Maximum Concentration and Horizontal Asymptote

The concentration C of a certain drug in a patient's bloodstream t minutes after injection is given by C(t)=50T divide by t^2 +25 a) Using your graphing utility, graph C=C(t). b) Determine the time at which the concentration is highest. c) Find the horizontal asymptote of C(t). What happe