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Optimization

Using Lagrange Multipliers to Find Extreme Values

Use Lagrange multipliers to find maximum and minimum values of the function subject to a given constraint or constraints. 1.)f(x,y,z)= xyz; x^2 + 2y^2 + 3z^2 = 6 2.)f(x,y,z)= x^2 + y^2 + z^2; x^4 + y^4 + z^4 = 1 3.)f(x,y,z)= x^4 + y^4 + z^4; x^2 + y^2 + z^2 = 1.

Profit

A local newspaper vendor sells papers for $0.50. The papers cost her $0.40, giving her a $0.10 profit on each one she sell. From past experience, she kows that 20% of the time she sell 100 Papers 20% of the time she sell 150 papers 30% of the time she sells 200 papers 30% of the time she sells 250 papers Assuming that sh

Profit Maximization - Transportation

Forbelt Corporation has a one-year contract to supply motors for all refrigerators produced by the IAC. ICA manufacures he refrigerators at 4 locations around the country: Boston, Dallas, Los Angeles and St. Paul. Plans call for the following number ( in thousands) of refrigerators to be produced at each location: Boston--50 D

Integer Programming

1. Integer Programming Problem Consider the following integer linear programming problem Max Z=3x1+2x2 Subject to: 3x1+5x2<=30 5X1+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 Z value for the optimal solution under integer

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

Finding maxima and minima, concave up and concave down.

Graph the function and locate intervals on which the function is increasing or decreasing, open intervals on which the function is concave up or concave down, and all inflection points. The function is: f(x) = x^(2) / x^(2) +4 Please show the graph and answer the questions. Thank you!

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.

Minimizing the Cost of Laying a Pipeline

Bill owns an oil well located 400m from a road. Bill wants to connect the well to a storage tank 1200m down the road from the well. It costs #35/m to lay pipe along the road and #50/m to lay it elsewhere. How should the pipeline be laid to minimize the total cost?

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

Finding the Max and Min Modulus

Find the max and min modulus if f(x) = z + 3i on the closed region defined by |z| < 2. I don't have clue as to where to start.

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.

Optimal Call Box Locations

Cumberland University is siting emergency callboxes on the campus to increase the safety for their students. The have determined that there are 7 areas that need coverage and 7 potential locations for the call boxes. (see below) Note that any call box location actually covers more than one area. Find the minimum numbe

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