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# Optimization

### Classification of Critical Points

Determine the intervals on which the following functions are increasing and decreasing and classify each of the critical points as a relative minimum, a relative maximum, or neither one. A) f(x)=3/4x^4+4x^3+6x^2+48 B) g(x)=x^6-6x^5-21x^4

### Management Science: Forecasting

6. The manager of the Petroco Service station wants to forecast the demand for unleaded gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 10 months: Month Gasoline Demand (gal) O

### Optimal Solution for Product Cost

I'm looking to understand how to determine the optimization for the following problem. Part One: What is the optimal solution for this problem? M&D Chemicals produces two products that are sold as raw materials to companies manufacturing bath soaps and laundry detergents. Based on an analysis of current inventory levels an

### Operations Research - Total Minimum Editing Time Problem

A manufacturing company has five jobs that must be completed as soon as possible. Six machines are available for doing the work, however the processing times for the various jobs varies depending on the machine doing the processing. The company wants to use an assignment method to determine which machine processes each job. Esti

### Determining an optimum production schedule

Shale Oil, located on the island of Aruba, has a capacity of 600,000 barrels of crude oil per day. The final products from the refinery include two types of unleaded gasoline; regular and premium. The refining process encompasses four stages: (1) The pure crude flows through a distillation tower that produces a feedstock

### Integer Programming using Excel Solver

26. The Roadnet Transport Company expanded its shipping capacity by purchasing 90 trailer trucks from a competitor that went bankrupt. The company subsequently located 30 of the purchased trucks at each of its shipping warehouses in Charlotte, Memphis, and Louisville. The company makes shipments from each of these warehouses to

### Optimizing the Use of Raw Materials for Profit

A factory uses raw materials x and y to produce products A and B Each unit of product A requires 4 units of x and 6 units of y Each unit of product B requires 5 units of x and 4 of y. On hand there are 30 units of x and 28 units of y. The profits on the sales of A and B are 6.5 per unit and 4.75 per unit, respectivel

### Linear Optimization Problems

I need help with these problems. Problems 8-4, 8-6 MUST use Excel's Solver to complete the problems. Note, the template is also attached for these 2 problems and must be solved using this template. 8-4 (Animal feed mix problem) The Battery Park Stable feeds and houses the horses used to pull tourist-filled carriages through

### Exponential and Adjusted Exponential Forecast and MAPD

Perform an Exponential Smoothing Forecast (a=0.3) and an Adjusted Exponential Smoothing Forecast (b=0.2) on the given data and forecast the demand for the month of November. Compare the accuracy of the two forecast methods using MAPD. [Please refer to the attachment for data].

### Optimisation for Running a Firebreak

A forest fire is burning down a narrow valley 3 miles wide at a speed of 40 feet per minute. The fire can be contained by cutting a firebreak through the forest across the valley. It takes 30 seconds for one person to clear one foot of the firebreak. The value of lost timber is \$4,000 per square mile. Each person hired is paid

### Algebra: Descriptive and Prescriptive Models

Explain the difference between descriptive and prescriptive (optimization) models. Please be detailed.

### Critical points for a ballistic projectile

If an object is thrown upward from 15 meters above ground with an initial velocity of 18 meters per second, then its height h above ground after t seconds after it is thrown is given by h(t)=-4.9tÂ²+18t+15 Use your calculator to answer the following (round to the nearest hundredth, if necessary): a) Ske

### Proof Using the Maximum Modulus Principle

Let f be continuous on a closed bounded region R and let it be analytic, and not constant throughout the interior of R. Assuming f(z) is not equal to 0 inside R (this assumption is easy since we may add a finitely large constant to f to avoid having it touch 0. Prove that |f(z)| has a minimum value m in R, which occurs on the bo

### Keeping crops healthy

Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown in the following table. Develop a 3-year moving average to forecast sales. Then estimate demand again with a weighted moving average in which sales in the most recent year are given a weight of 2 and sales in the other 2

### Exponential smoothing

Sales of Cool-Man air conditioners have grown steadily during the past 5 years: The sales manager had predicted, before the business started, that year 1's sales would be 410 air conditioners. Using exponential smoothing with a weight of Coefficient = 0.30, develop forecasts for years 2 through 6. YEAR SALES

### Forecasting time series based on Moving average

Please provide tutorial help involving moving averages. Moving averages often are used to identify movement in stock prices. Daily closing prices (in dollars per share) for a large company (Tab STOCK PRICES data set) a) Use a 3-time period moving average to smooth the time series. Forecast the closing price for the n

### Regression Optimization to Determine Price

1. You decide to buy'a diamond ring. To make sure you get a quality ring for your money, you educate yourself on things to look for in buying a diamond. After some research on the web, you learn about the 4C's of diamonds: cut, clarity, color and carat. You decide the ring you want to purchase will have a a round-cut diamond and

### Compute and figure answer as directed by question.

Megley Cheese Company is a small manufacturer of several different cheese products. One of the products is a cheese spread that is sold to retail outlets. Jason Megley must decide how many cases of cheese spread to manufacture each month. The probability that the demand will be six cases is 0.1, for 7 cases is 0.3, for 8 cases

### Linear Programming (LP)

Need LP tutorial help involving optimization and the use of Solver. Solve the following modifications of the Tatham Capital Budgeting model (solve each part independently of the others) (a) Suppose that at most two of the project 1 - 5 can be selected. write the appropriate algebraic constraint and solve. What is the new

### Linear Optimization: The international Chef, Inc.

The international Chef, Inc markets three blends of oriental tea: premium, Duke Grey and Breakfast. THe firm uses tea leaves from India, China, and new domestic California sources. Net profit per pound for each blend is \$.50 for premium, \$.30 for Duke Grey, and \$.20 forbreakfast. The firmsregular weekly supplies are 20,000 pound

### Forecasting Smoothing Constants

Exponential smoothing with smoothing constant ? = 0.1. Use the actual value of the first period as the starting forecast for the second period. Time Period Actual Value Exponential Smoothing (? = 0.1) Forecast 1 211 2 228 211.00 3 236 4 241 5 242 6 227 7 217 8 203 b.) Exponential smoothing with smoothing

### Optimization Involving Restriction and Relaxation

Optimization involving restriction and relaxation. Please read the pdf file and use the provided Excel spreadsheet for the solution. Please, no integer solutions. MUST include objective function! Must do questions 1 and 2.

### Product mix linear optimization

Three products a,b,c. Net profit ten dollars for each a, 7.50 each b. 4 for each c. Each a needs 5 hrs production time one hour packing time. B is 4 and .75 c is 3 and .2 100 hours production available. 200 hours packing time A can be no more than 50 percent of mix. C must be at least 20 percent Maximize profits.

### Linear Programming for profit optimization

The Exeter Company produces two basic types of dog toys. Two resources are crucial to the output of the toys: assembling hours and packaging hours. Further, only a limited quantity of type 1 toy can be sold. The linear programming model given below was formulated to represent next weekÃ¢Ã¢?Â¬Ã¢?Â¢s situation. Let, X1 = Amount o

### Graphical Approach for Solving Linear Programming Problems

This is liner programming problem for optimization of an objective function subject to some liner constraints. There are two profit maximization problems and two cost minimization problems. For each problems below complete the following: a) Graph and label every inequality. State the scale used on both axes. b) Shade the

### Mathematics: Linear Optimization

The International Chef, Inc. markets three blends of oriental tea: premium, Duke Grey, and breakfast. The firm uses tea leaves from India, China, and new domestic California sources. Tea Leaves (Percent) Quality Indian Chinese California Premium 40 20

### Inflection, Minimum and Maximums of a Function

Please see the attachment. Answer the following questions for the function f(x)=x Square root(x2+25) it is x^2+25 inside the square root defined on the interval [-7,4]. A. f(x) is concave down on the region ____ to _____ B. f(x) is concave up on the region _____ to _____ C. The inflection point for this function is

### Finding the optimal solution

Lifeguards are assigned to work 5 consecutive days a week and have 2 days off. They have to have this number daily, so how do I set this up on a spreadsheet? sun 18 mon 17 tues 16 wed 16 thur 16 fri 14 sat 19 How do I find the optimal solution?

### Simplex Maximization Story Problem

A farm co-op has 6001 acres available to plant with corn and soybeans. Each acre of corn requires 9 gallons of fertilizer/herbicide and 3/4 hour of labor to harvest. Each acre of soybeans requires 3 gallons of fertilizer/herbicide and 1 hour of labor to harvest. The co-op has available at most 40,500 gallons of fertilizer/herbic

### Forecast monthly demand for products

Monthly demand for a product has been as follows in the last 2 months. July 55 units August 61 units What is the forecast for September using exponential smoothing with alpha = 0.2 if the forecast for July was 50 units?