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# Optimization

### Network Representation of the Distribution System

A company imports goods at two ports: Philadelphia and New Orleans. Shipments of one product are made to customers in Atlanta, Dallas, Columbus, and Boston. For the next planning period, the supplies at each port, customer demands, and shipping costs per case from each port to each customer are follows:

### Integer Programming

Solve the following problem: Max X + 2Y s.t. 6X + 8Y < 48 7X + 5Y > 35 X, Y > 0 Y integer a. Find the optimal solution to the LP Relaxation. Round down to find a feasible integer solution. Is this solution optimal? b. Find the optimal solution.

### Forecasting

Mathematics, topic: FORECASTING; from book Quantitative Methods. I need help for problem number 8. Please look at the attachment; I will need help for problem 8; in Chapter 15. (you will see the problem on two different file, file 1 and file 2, I also add some example on file 3). The second problem is on page 706, and I need he

### Optimization - The Department of the Navy has been downsizing and is looking for cost savings opportunities to meet mandated congressional budget cuts. One suggestion under consideration is to change the make up of content of Navy sea rations, the canned food supplies containing certain minimum quantities of Vitamin A, Vitamin D, iron, and other nutrients, which combat troops carry into battle. ...

The Department of the Navy has been downsizing and is looking for cost savings opportunities to meet mandated congressional budget cuts. One suggestion under consideration is to change the make up of content of Navy sea rations, the canned food supplies containing certain minimum quantities of Vitamin A, Vitamin D, iron, and

### Integer Linear programming problems

1. Consider the following integer linear programming problem. Max Z = 3x1 + 2x2 Subject to: 3x1 + 5x2 <= 30 4x1 + 2x2 <= 28 x1 <= 8 x1, x2 >= 0 and integer The solution to the linear programming relaxation is: x1 = 5.714, x2= 2.571. What is the optimal solution to the integer linear programming problem? State the value

### Quantitative Methods - We manufacture refrigerators in Nashville, TN.

This is one problem. I need to know if the question is an accounting, break-even analysis, or simulation problem and why or why not. Please answer all the questions. We manufacture refrigerators in Nashville, TN. The petroleum crisis has raised the price of gasoline to \$3.75 for regular and diesel to \$4.35 per gallon. I

### Quantitative Methods Using Integer Programming

This problem has to do with integer programming. See the attached Excel file for proper formatting. Wk 8 Apene plans to purchase 1350 PCs. Three sources are being considered. (Dealt, ICN, and McElectric). Each charges a variable cost per computer plus a fixed delivery and installation cost. See the table below.

### QUANTITATIVE METHODS: Forecasting

Show all work, where appropriate in using Excel (no version higher than 2003), PLEASE INCLUDE ALL FORMULARS IN CELLS WHERE CALCULATIONS ARE MADE. Recent past demand for product ZXT is given in the following table: Month Actual Demand February 20 March 22 April 33 May 35

### Practice on Maximum and Minimum, Profit maximization

10 practice questions on Maximum and Minimum values (2) Find the absolute maximum value and the absolute minimum value, if any, of the following function. (If an absolute maximum/minimum does not exist, enter NONE in that blank.) g(x) = -x^2 + 2x + 10 (6) Lynbrook West, an apartment complex, has 100 two-bedroom units. The mo

### Find the optimal order quantity

The Super Discount store (open 24 hours a day, every day) sells 8-packs of paper towels, at the rate of approximately 420 packs per week. Because the towels are so bulky, the annual cost to carry them in inventory is estimated at \$.50 per pack. The cost to place an order for more is \$20 and it takes four days for an order to arr

### The nuclear plant currently has 350 fully trained workers. They need to know how many worker are need to be trained for the remainder if the year. 1. Formulate this staffing problem using LP. 2. Solve the problem. How many trainees must begin each month? 3. Submit the problem in Excel Solver.

Dear OTA, Please provide me a solution with detailed explanation. Thanks The nuclear plant currently has 350 fully trained workers. They need to know how many worker are need to be trained for the remainder if the year. Month Personnel Hours Needed August 40,000 September 45,000 October 35,000 November 50,000 D

### Decision Making :Forecasting

We manufacture wood front doors with glass inserts We \$5 of wood, \$2 of glass, \$10 of metal fixtures, and \$1.50 of plastics We assemble and finshed the wooe, cut the glass, and assemble the product in our two plants (Idaho and North Carolina). One plant ships to customers west of the Mississippi, the other

### Find dimensions of maximum volume of suitcase

An international airline has a regulation that each passenger can carry a suitcase having the sum of its width, length and height less than or equal to 135 cm. Find the dimensions of the suitcase of maximum volume that a passenger may carry under this regulation.

### Maximum Volume of a Box

A parcel delivery service will only accept a package for delivery if the length plus the girth (distance around the package) does not exceed 108 inches. Find the dimensions of a rectangular box with square ends that maximizes the volume, and state the maximum volume.

### Quantitative Methods - The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet.

I need help finding a solution to the below problems for Quantatitive Methods. 15. The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. The company operates one "8 hour" shift per day. Therefore, the production time is 480 minutes per day. During

### XieCorp is a pc solutions provider that is looking to expand its operations. - Balance Income Statement

XieCorp is a pc solutions provider that is looking to expand its operations. Currently it has \$500K (K=thousand) to invest in an upgrade in facilities. The goal is the hire additional staff to acquire new customers. Last year 20XX XieCorp made \$13M (M=million) in total revenues. Their expenses were 65% of revenue and they were t

### Goal Programming - First West Chemical Company

Need a lot of direction to solve this problem. Thank you. First West Chemical Company produces two chemical ingredients for pharmaceutical firms; formula X and formula Y. Production of each ingredient requires two processes. A unit of Formula X requires 4 hours in process 1 and 3 hours in process 2. A unit in formula Y requ

### Suppose Charlie O'Brien hits a baseball straight upward at 150 ft/sec from a height of 5 ft.

Foul ball. Suppose Charlie O'Brien hits a baseball straight upward at 150 ft/sec from a height of 5 ft. Use the formula to determine how long it takes the ball to return to the earth. Use the graph to estimate the maximum height reached by the ball. See attachment.

### Baseball umpiring crews are currently in four cities where three game series are beginning.

Baseball umpiring crews are currently in four cities where three game series are beginning. When these are finished, the crews are needed to work games in four different cities. The distance between each of the cities where the crews are currently working to the cities where the new games will begin are shown in the following ta

### Maximum Volume of a Right Circular Cylinder

What is the maximum possible volume of a right circular cylinder with a total surface area (including the top and the bottom)? 600 pi in^2 Find the exact coordinates of the inflection points and critical points of the function (Figure 15.1) on the interval (-10, 10) f(x)= 2x^3+ 3x^2- 180x+ 150 Find dx/dt given

### Quantitative Methods : Moving Averages, Exponential Smoothing and Forecasting

1. The Snyder company percentages of all shipments that were received on time over the past 12 months are 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84 and 83... A. Compare a 3-month moving-averages forecast with an exponential smoothing forecast for a = 0.2 Which provides a better forecast? Part B. What is the forec

### Modeling, Trends and Forecasting

Suppose that the function represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2000. Carry all calculations to six decimals on each intermediate step when necessary. a) Use this model to approximate the percentage of spam in the year 2003. b)

### Optimization and Closest Point on a Line

1. Minimize the perimeter of rectangles with area 25 cm^2 . Is there a maximum perimeter of rectangles with area 25 cm? 2. Find two numbers whose difference is 100 and whose product is a minimum. 3. If 1200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the bo

### Dynamic Programming : Reliability of Components

An electronic device consists of 3 main components arranged in series so that the failure of one component causes the failure of the whole device. The reliability of the device can be improved by having up to, 2 standby units in parallel for each component. The total capital available for the design is £10,000. The reliability

### Maximum Revenue

Please see attached file for full problem description. The revenue derived from the production of x units of a particular commodity is million dollars. What level of production results in maximum revenue? What is the maximum revenue? a. a. Maximum at x = 8 and maximum revenue is R(8) = 32 (million dollars) b. b. Maxi

### Detemine the maximum value of Z subject to given conditions.

Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 <= 136 3x1 + 4x2 <= 36 x1, x2 >= 0 and integer What is the optimal solution? And, Z = ?

### Modeling and Optimization : Staffing Levels

Scheduling staff. You are the director of the Computer Center for Gaillard College and rewponsible for scheduling the staffing of the center, which is open from *a.m. until midnight. You have monitored the usage of the center at various times of the day and determined that the following number of computer consultants are req

### Whoppy Soft Drink Company Production and Optimal daily output for regular and diet

The production manager for the Whoppy Soft Drink Company is considering the production of two kinds of soft drinks: regular and diet. The company operates one "8 hour" shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup, is limited to maximum pr

### Non linear Optimization

Ordering fuel. Three liquid fuels are stored in tanks for use in a blending process. Each fuel is characterized by a demand rate, a fixed replenishment cost, and a unit cost. Inventory carrying costs are assessed at the rate of 12 percent per year. In order to save money on insurance rates, the operating policy is to limit

### 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