Explore BrainMass
Share

# Optimization

Optimization is the selection of a best element from some set of available alternatives. An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. Optimization is finding the best available value of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.

An optimization problem can be represented in the following way:

Given: a function f: A→R from some set A to the real numbers

Sought: an element x0 in A such that f(x0) <= f(x) for all x in A (“minimization”) or such that f(x0) >= f(x) for all x in A (“maximization”).

This formulation is called an optimization problem or mathematical programming problem. Many real world applications are modeled in their general framework.  By convention, the standard form of an optimization problem is stated in terms of minimization, unless both of the objective functions and the feasible region are convex in a minimization problem.

### Non-linear programming problem find minimum profit using excel

The personel director of a company that recently absorebd another firm and is now downsizing and must relocate five information specialist from recently closed locations . Unfortunately, there are only three positiins available for five people. Salaries are fairly uniform among this group ( those with higher pay were already gi

### Linear programming to find maximum profit using excel solver

WORLEY FLUID SUPPLIES PRODUCES THREE TYPES OF FLUID HANDLING EQUIPMENT CONTROL VALVES, METERING PUMPS AND HYDRAULIC CYLINDERS/ ALL THREE PRODUCTS REQUIRE ASSEMBLY AND TESTING BEFORE THEY CAN BE SHIPPED TO CUSTOMERS CONTROL VALVE METERING PUMP HYDRAULIC CYLIND

### Network for Subcontractor and Linear Model for Minimizing Costs

A mechanical contractor pays his subcontractors a fixed fee plus mileage for work performed. On a given day, the contractor is faced with three mechanical jobs associated with various projects. Each subcontractor will have enough time to work on up to two projects during the day. Each project should be completed by exactly two s

### Network Representation and Linear Transformation

The distribution system for a company consists of two plants, three warehouses, and three customers. Plant capacities and shipping costs per unit (in \$) from each plant to each warehouse are as follows on Exhibit A attached. Customer demand and shipping costs per unit (in \$) from each warehouse to each customer are as follow

### Sample Solution: Linear optimization: Inventory Management

Sales per year 10,400 cd's Mfg/Purchasing Costs She buys from supplier >= 1000 at \$4.45 ea CD She buys from supplier <=1000 at \$4.50 ea CD Delivery Charge from her supplier is \$10/shipment regardless of size She pays Finance Rate annual interest rate 15% She pays NYS Property Tax 5% on Annual Inv Val

### Stackhouse Corporation Linear Programming

Stackhouse Corporation makes a product which is essentially an assembly consisting of the height of two parts. Parts have been measured and classified by their deviation from their nominal dimension in thousandths of an inch. The current inventory of the two parts at various size deviations is tabled in the attached file. A cust

### Markov Chain Problem with Four Parts

The beginning of each day, patient in a hospital is classified into one of three conditions; good, fair, or critical. At the beginning of the next day, the patient will either continue to be in the hospital and be in good, fair or critical condition or the patient will be discharged in one of three conditions: improved, unimpro

### Woodworking Company LP Problem

See attached file - I need to answer all questions while showing all the work in Excel using Solver. I am lost :( Hope you can help...thank you!

### formulating a linear programming model and solving using Excel

Consider the following transportation problem: To(cost) From 1 2 3 Supply A \$6 \$9 \$100 130 B 12

### Box Material Optimization

U-Pack-Em sells cardboard boxes for the do-it-yourself mover. Their most popular size has a volume of 2 cubic feet. As shown in the figure below, the top and bottom are made using four flaps. The price of cardboard is \$0.20/ft'. What are the raw materials cost and dimensions for the cheapest box that can be manufactured? (Be

### Linear/integer programming model

Solver does not return a solution that makes sense to me. Particularly the highlighted parts of the worksheet. I don't know why, but Solver seems to ignore my "binary" constraint with regards to keeping plants open or closed and for some reason Solver does not return transportation cost values. Are you able to point me in the

### Calculate the monthly payment for a car purchase

Answer the following questions and add the answers to the attached excel workbook please do not delete the contents that are already imputed 1. The area of a triangle is equal to ½ the length of the base times the height of the triangle. Use the capabilities of Excel so that when you input the lengths into O2 and P2, the A

### The solution gives detailed steps on solving an optimization problem: finding the minimum dimension and cost for given volume and unit price. All formula and calculations are shown and explained.

The problem is looking find the minimum material and dimensions needed to build a box that has a volume of 2 cubic ft. The box has to have a volume of 2ft3. The box is folded and has 4 flaps on the top and bottom as shown below. The price of material to build the box is \$2/ft2. What are the material cost and dimensions to build

### In first problem, corresponding to given cost function, optimal size of the production to be estimated. In the second problem, expenditure function is optimized to maximize the profit

1) The cost per unit produced at a certain facility is represented by the function UC = 2x^2 - 10x + 50, where x is in thousands of units produced. For what value of x would unit cost be minimized (other than zero)? What is the minimum cost at this volume? Show that the value found is truly a minimum. 2) Advertising expenditu

### Max values of a function in a given interval

Find the maximum of f(x) = x^4 = 6x^3h + 11x^2h^2 - 6xh^3 at [0,3h]

### Statistical Analysis: Linear Optimization

Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are given in the following table. Bean Cost Available Pounds 1 0.5 500 2 0.7

### Linear Optimization - The Schutzberg Brewery Problem

6. Making Beer. The Schutzberg Brewery has received an order for 1,500 gallons of 3-percent beer (that is, 3 percent alcoholic content). This is a custom order because Schutzberg does not produce a 3-percent product. They do brew the following products. Product Percent Alcohol Cost per Gallon Free 0.25

A brand manager of Company A must determine how much time to allocate to radio and TV advertising for next month. Market Research have given estimates of the audience exposure for each minute of advertising in each medium, which it would like to maximize. Costs of minutes of advertising are known, and the manager has a budget of

### Linear Optimization Model: Toys

Super Toys Company makes to radio-controlled cars, Fast and SuperFast. They can sell all they make. Both models have the same components. Two of these can be obtained only from a single supplier. For next month, the supply of these is limited to 4000 of component X and 3500 of component Y. The following table provides details o

### Integer Programming Problem: Package Express Carrier

A package express carrier is considering expanding the fleet of aircraft used to transport packages. There is a total of \$220 million allocated for purchases. Two types of aircraft may be purchased - the C1A and the C1B. The C1A costs \$25 million, while the C1B costs \$18 million. The C1A can carry 60,000 pounds of packages, whil

### Linear Optimization Model

Please assist me in understanding the linear optimization model in the attached document. How many of each type of air compressor should the company produce to maximize profit? a. Formulate and solve a linear optimization model using the auxiliary variable cells method and explain the sensitivity information. b. Solve the m

### Ellipses and Optimization

Find the point on the ellipse x^2 + y^2/4 =1 closest to the point (5,7). The minimum distance is achieved at (x*, y*) = (___,___ ) This minimum distance D* = ___ P.S.- The answer is not (0.4) and min distance of 7.0711

### Rate of change and the chain rule

A rocket ship is speeding away from the sun. In convenient units, the radiation R inside the ship is given by R = 1/x^2, where x is the distance to the sun. This distance x, as a function of time t in hours, is given by x = 12t+ 2. How far is the ship from the sun when the radiation level is decreasing at a rate of 3 units

### Optimization of Grafting an Artery

A surgeon is faced with the problem of grafting an artery. She wishes to minimize the resistance to the resulting flow. The resistance R to the laminar flow in a pipe L is given by Poiseuille's law: R = L/ r^4 This is where L and r are the length and radius respectively of the pipe. The graft must run from a main artery of r

### Optimization and Operations Research

Two players fight a duel as follows. Each has a (silent) gun with a single bullet. They begin 2n=10 paces apart. At a signal, each may fire. If either is hit or if both fire, the game ends. Otherwise, both advance one pace so they are now 2n-2 paces apart and again wait for the signal. The game ends in any case after at most n s

### Finding Maximum and Minimum Values

Questions: A) Find all critical points of f(x)=x^5+5x^4-35x^3 and classify each as a relative minimum, relative maximum or neither one. B) Find the absolute maximum and minimum values of f(x)=2x^4-16x^3-32x^2 on the interval [-3,2].

### Optimal solution using the graphical method

Consider the following Linear programming model Maximize: Z = 3x + 2y Subject to: 2x + 1y =< 60 2x + 3y =< 120 x, y =< 0 Find the optimal solution using the graphical method. Identify the feasible solution area and the optimal solution on the graph.

### Linear Model and Optimal Solution

Problem 49 An oil company in Texas has three oil wells with capacities of 93, 88 and 95 thousand barrels per day respectively. The company also owns five refineries along the Gulf Coast, all of which have been operating at stable demand levels. Three pump stations have been built to move the oil from the wells to the refineries

### Operations Research and Optimization

Consider the linear programming problem Minimize x_1+x_2 Subject to 2 x_1 + x_2 leq 0 x_1 - 2x_2 geq 0 x_1/3 - x_2 =10 You are to transform this problem to a form suitable for feeding to programs expecting the standard forms below. In each part, record the matrices f, A, and b suitable for feeding to a software

### Solve: The Maximum and Minimum Prices of Stock

Suppose that a company decides to raise capital by selling stock. Over the next 30 years the average monthly price of the stock fluctuates according to the rule S(t)=0.25t^1.20-0.90t+65.85 where S(t) is in dollars per share and t is the number of months since the stock was first offered for sale (this means that S(t) is only val