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Optimization

Maximizing area of a fenced garden

A. A rectangular garden is to be fenced in and divided into three parallel sections. the fencing for the boundary costs $20 per foot whereas fencing for the dividing fences costs $5 per foot. Consider the problem of finding the dimensions of the largest garden possible if the gardner can spend $2000 for the fencing. Find the va

Optimization Problem

We want to create a box with a square base made out of cardboard. The top will be double thickness and the bottom triple thickness. We want the box to hold 400 cubic inches and to use the least amount of cardboard. a) Write an expression for C (the area of cardboard needed) in terms of s,the width of the base, and h, the heig

Decision-Making, Decision Variables, Modeling and Optimization

You need to decide where to locate call centers and determine the routing of calls to achieve the lowest total cost. You are considering seven cities in which to locate call centers. You know the average cost incurred if a call is made from any of these cities to any region of the country. (See first table below) You also know t

Integer programming problems

Prob 1 Blinkies is the 24-hour hot spot in town. The work schedules start every three hours and are listed below with the number of staff members neede for each three hour period. Staffers may be assigned 6 hour shifhts (for which they are paid $50) or 9 hour shifts (for which they are paid $65) A manager is rquired for eac

Maximizing the Volume of an Open Top Box

1.You are to design a container box by cutting out the four corners of a square cardboard sheet that is 1600 cm2 in area. The box must have a square base and an open top. Determine the dimensions of the box that give maximum volume. 2.Sketch the graph of the function f(x)=x2+4 Identify the following features of the graph:

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

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

What is the minimum cost and associated routing

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 capacit

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

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.

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.