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Optimization

Optimization Word Problems

1. A rectangular field is going to be enclosed and divided into two separate rectangular areas. (The areas do not have to be equal.) Find the minimum fencing that is required if the total area of the field is 1200 m2. 2. A closed cylindrical container needs to have a volume of 128pie dm3. Find the dimensions if the total are

Asymptotes and Maximum and Minimum Values

1.Determine the vertical asymptotes for the following function. Draw a sketch to show from which side the function approaches. y=__x2-49 x2+9x+20 2.Determine the horizontal asymptote for the following function. Draw a sketch to show whether the function is above or below the asymptote as x→∞. y=__8x2

Forecasting problem using Excel modules addin

11-19 Sales of Cool-Man air conditioners have grown steadily during the past five years, as shown in the following table. Year Sales 1 450 2 495 3 518 4 563 5 584 a) using exponential smoothing constants of 0.3, 0.6, and 0.9, develop forecasts for years 2 through 6. The sales manager had predicted, before the business

Forecasting model using Excel Modules addin

11-13 Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown in the following table: Year Bags (in thousands) Year Bags (in thousands) 1 4 7 7 2 6 8 9 3 4 9 12 4 5 10 14 5 10 11 15 6 8 a) develop two-year, three-year, and four-year moving averages to forecast demand

Forecasting problem using Excel Modules add in

Uses Excel Modules Addin to solve. Add in is attached 12-16 Barbara Bright is the purchasing agent for West Valve Company. West Valve sells industrial valves and fluid control devices. One of the most popular valves is the Western, which has an annual demand of 4,000 units. The cost of each valve is $90, and the inventory car

Dividend valuation model and wealth maximization

Eastern Telecom is trying to decide whether to increase its cash dividend immediately or use the funds to increase its future growth rate. It will use the dividend valuation model originally presented in Chapter 10 for purposes of The model was shown as Formula 10-9 and is reproduced below (with a slight addition in definition o

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

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

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

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 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

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

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

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,

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.

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

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

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