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# Optimization

### Exponentially smoothed forecast for period 8

1. In period 7 the exponentially smoothed forecast was 50 and the actual demand was 49. If alpha is equal to 0.10, what is the exponentially smoothed forecast for period 8? 2. Number of hours required per unit is 4 hours and there are 8 working hours per day. There are 20 working days in each month. Find the number of workers

### Find the Maximum Area

A city decides to make a park by fencing off a section of river front property. Funds are allotted to provide 80 meters of fence. the area enclosed will be a rectangle but only 3 sides will be enclosed by fence. The other side will be bound by the river. What is the maximum area that can be enclosed?

### Forecasting Models

John S has developed the following forecasting model y=36+4.3X 1 (lower case 1) where y = demand for k10 air conditioners X1= outside temperature in ( F ) (a) forecast the demand for k10 when the temp is 70 degrees F (b) what is the demand for 80 degrees F (c) what is the demand for 90 degrees F

### Use dynamic programming to find the longest path.

Consider the graph in the attachment. Use dynamic programming to find the longest path from node 1 to node 7. What are the states and stages? What is the recursive function?

### A number of problems using Nyqusit criteria to determine the minimum bandwidth requirements of digital communications channels

1st problem: A digital signaling system is required to operate at 9600 bps. If a signaling element encodes a 8-bit word, what is the minimum required bandwidth of the channel? 2nd problem: A given modem represents eight bits with each signaling element. How many different signaling elements are required? What would be

### Maximum Profit

Natural Furniture Company manufactures three outdoor products, chairs, benches, and tables. Each product must pass through the following departments before it is shipped: sawing, sanding, assembly, and painting. The time requirements (in hours) are summarized in the tables below. The production time available in each departm

### Quantitative Methods Optimal Location

2) An airline wants to begin operations in a new city. Two cities, A and B, are being considered. The airline will locate in the city whose airport has the lowest landing fees. These are determined by demand. The cost, in tens of thousands of dollars per year, is summarized in the table below.

### Branch and Bound

Can you please assist me with working out this problem? Thanks!

### Branch and Bound for Tree Integer

Solve the following problem using Branch and Bound.Show the B&B tree.If node is fathomed,indicate why it is fathomed.Provide the sequence of problems solved,. eg. P1-P3-P4, etc.Clearly indicate what the optimal solution is.Note: x4 does not have to be integer.After solving the root node, branch on x1 first. Max Z=4x1-2x2+7x3-

### Optimization Problem

Develop and solve a linear optimization model to determine the optimal mix to maximize profit, and write a short memo to the president, Kathy Chung, explaining the sensitivity information in language that she can understand.

### Provide an integer programming model for this problem.

Corsouth Mortgage Associate is a large home mortgage firm in the Southeast. It has a pool of permanent and temporary computer operators who process mortgage accounts, including posting payments and updating escrow accounts for insurance and taxes. A permanent operator can process 220 accounts per day, and a temporary operator ca

### What is forecasting? What information is forecasted at your organization?

What is forecasting? What information is forecasted at your organization? Which forecasting methods are used at your organization? What information at your organization is not currently being forecasted that could be forecasted to increase productivity or decrease waste?

### Absolute maximum and minimum values

1. Given f(x) = x [(x+3)^1/2] a) Find the intervals on which f is increasing and decreasing. b) Find any relative extrema that f may have. c) Find the intervals of concavity and inflection points of f. d) Sketch the graph of f. 2. find the absolute maximum and minimum values of f(x) = ln(x^2 + x + 1) on the interval [-1,

### Maximum Modulus Principle

See attached a pdf file. You can find more Mobius transformation information from John Conway - Functions of One Complex Variable I or Serge Lang - Complex Analysis or other Complex Analysis books. Problem of Schwarz's Lemma 1. Suppose f: D → ¢ satisfies Re f(z) ≥ 0 for all z in D and suppose that f is analytic and

### Ranges of optimality

Answer Questions 2 and 3 based on the following LP problem. Maximize 2X1 + 5X2 + 4X3 Total Profit Subject to X1 + X2 + X3 > 150 At least a total of 150 units of all three products needed X1 + 3X2 + 2X3 â?¤ 300 Resource 1 2X1 + X2 + 2X3 â?¤ 250

### Area Maximization for Fencing a Yard

Jason plans to fence a rectangular area with 120 m of fencing. Allowing w to be width and l to be length of our rectangular area, we have, therefore, perimeter = 2w + 2l = 120, or l = 60 - w. Knowing that our area A is wl, or A = w(60-w), what selection of width w will maximize our area A?

### Optimal solution for Blacktop Refining in Montana

Can someone teach me how to formulate the Optimal solution for this problem without using Excel? The constraints I figured out are: Copper .2x1 + .3x2 >= 8 Zinc .2x + .25x2 >= 6 Magnesium .15x1 + .1x2 >= 5 What is the next step? Blacktop Refining extracts minerals from ore mined at two different sites in Montana.

### Dual problem case

Please help with the following linear programming problems. Provide step by step calculations. Consider the primal problem Min c1x+ c2x2 + c3x3 s.t a11x1 + a12x2 + a13x3 >=b1 a21x1 + a22x2 + a23x3 >=b2 a31x1 + a32x2 + a33x3 >=b3 x1, x2 and x3

### Investment: government bonds, mutual funds, money market funds

An investor has at most \$40000 to invest in government bonds, mutual funds, and money market funds. The average yields for the government bonds, mutual funds, and money market funds are 4%, 11% and 9% respectively. The investor's policy requires that the total amount invested in mutual and money market funds not exceed the am

### Decision Models

Pharmgen Corporation is a pharmaceutical company developing a new drug to fight cancer. It recently discovered a rival company is just one year away from finishing its development in a similar drug which will take away some market share if released. Pharmgen identifies two possible scenarios. The first one, which has a probabili

### Trail Time blend cost minimization

FarmFresh Foods manufactures a snack mix called TrailTime by blending three ingredients: a dried fruit mixture, a nut mixture, and a cereal mixture. Information about the three ingredients (per ounce) is shown below. Ingredient Cost Volume Fat Grams Calories Dried Fruit .35 .25 cup 0 150 Nut Mix

### Decision Analysis Problem for Anna Tabara

Anna Tabara has three major routes to take to work. She can take Market street the entire way, she can take seveal back streets to wok, or she can use the expressway. The traffic patterns are very complex however. Under good conditions, Market street is the fastest route. When Maket is congested, one of the other routes is usual

### Maximization of a Function

Assume that you have solved up to the point where your last pivot and subsequent row operations have yielded the Tableau below. Assume X, represents raisin bread and X2 represents raisin cakes. Normalize the Tableau (optional) and determine results. What are the Basic Feasible Variables? What are the Basic Feasible Solutions

### Description of Optimal Order Quantity

Please see attachment for picture... The bookstore at a university purchases sweatshirts emblazoned with the school name and logo from a vendor. The vendor sells the sweatshirts to the store for \$38 apiece. The cost to the bookstore for placing an order is \$120 and the carrying cost is 25% of the average annual inventory valu

### Inventory Management analysis problem

The purchasing manager for the Atlantic Steel Company must determine a policy for ordering coal to operate 12 converters. Each converter requires exactly 5 tons of coal per day to operate, and the firm operates 360 days per year. The purchasing manager has determined that the ordering cost is \$80 per order and the cost of hold

### Inventory Management

The Petroco Company uses a highly toxic chemical in one of it's manufacturing processes. It must have the product delivered by special cargo trucks designed for safe shipment of chemicals. As such, ordering (and delivery) costs are relatively high, at \$2,600 per order. The chemical product is packaged in 1-gallon plastic cont

### Linear Optimization (blending)

Develop a linear programming model with the data from tables 1-5 Make or Buy(maximize profit /minimize cost) There are Four orders for the next 90 days Orders are to be Completed 90 Days Products are shown in Table 1. The orders are shown in Table 2 Table 3 lists the amount of plate steel required to produ

### Find consumer's surplus at maximum profit level.

A monopoly has a total cost function c = 250 + x^2 + 5x for its product, which has demand function p = (-1/3)x^2 - 2x +30. Find the consumer's surplus at the point where the monopoly has a maximum profit.

### AvAir - Forecast

AvAir, a regional airline, reported miles flown data as shown in Table 1, below. In January 2002 AvAir added aircraft to its fleet and changed the method of scheduling maintenance. REVENUE SEAT MILES (000's) AVAILABLE SEAT MILES (000's) 2006 2007 2006 2007 January 10,5