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# Optimization

### Minimization Problem - Simplex Method for a blending decision in developing a new cat food

The Corporation faces a blending decision in developing a new cat food. Two basic ingredients have been combined and tested, and the company has determined that to each can of cat food at least 30 units of protein and at least 80 units of riboflavin must be added. These two nutrients are available in two competing brands of anim

### Operational Optimization, Queueing, Linear Programming, Logistics, Flow Charts and Productivity

1. A company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used five workers, who produced an average of 80 carts per hour. Labor cost was \$10/hour

### Java Programming : Switch Statements and Switch Blocks

If x is currently equal to 5, what will the value of x be after the switch statement executes? Answer is 11. Please explain.The switch statement is switch (x) { case 3: x+=1 case 4: x+=2 Case 5: x+=3 case 6: x++; case 7: x+=2 case8: x-- case 9: x++

### 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

### Forecasting problems gasoline time series

1. Gasoline sales time series Week Sales (000s of gallons) 1 17 2 21 3 19 4 23 5 18 6 16 7 20 8 18 9 22 10

### 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&#8594;&#8734;. 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

### Evaluating the Maximum and Minimum Values of a Function

Find the maximum and minimum values of the function f (x,y, z) = x + 2y subject to the constraints y^2 + z^2 = 144 and x + y + z = 4. Maximum value is ____, occurring at (____, ____, ____). Minimum value is ____, occurring at (____, ____, ____).

### Question about Maximum and minimum volumes of a rectangular box

Find the maximum and minimum volumes of a rectangular box whose surface area equals 8000 square cm and whose edge length (sum of lengths of all edges) is 480 cm. See attached file for full problem description.

### Solve the following problem for the optimal number of clerks:

There are approximately 300 customers shopping in Fackert Department Store in Mexico City between 9 a.m. and 5 p.m. on Saturdays. When deciding how many cash registers to keep open each Saturday, owner Susanna Fackert considers 2 factors: customer waiting time (and the associated waiting cost) and the service costs of employing

### Managerial Finance - questions/problem about General Electric Corporation and Tyco International

A. The following is the scenario you should consider when answering: General Electric Corporation and Tyco International are both classified as "conglomerates" (having many diversified business lines). General Electric has pursued a conservative growth strategy by focusing on being the number one or number two in each indu

### Lagrange Multiplier Optimization

Please explain the two constrained optimization problems using a lagrangian multiplier. Problem one as follows: Maxamize f(x,y)= x ^1/3 y^2/3 subject to x+2y=100 The next one is a three variable problem max f(x,y,z)=x ^ 1/4 y ^ 2/4 z ^ 1/4 subject to 2x+2y+2z = 100 I understand how to set the problem up with parti

### 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

### Finding the relative maximum point of function.

Find the relative maximum point for the function f(x) = -x^3 + 3x^2 +24x +5

### 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

### Recursive definitions

(See attached file for full problem description) --- Give a recursive definition of a) of the functions max and min so that mx{a1,a2,..an and min {a1,a2,...an} are the maximum and minimum of the n numbers a1,a2,...an respectively b) prove that f12+f22+..fn2 = fnfn+1 whenever n is a positive integer fn is the Fibonacci sequ

### 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