Sheep fencing problems Calculus wall sheep fencing A farmer has a field in which there is a very long straight wall. The farmer also has 340 metres of.

Slides:

Advertisements

Similar presentations

An Area Problem An Investigation.

Advertisements

problems on optimization

Quadratic Word Problems

Max/min Finding Roots. You should know the following about quadratic functions: How to graph them How to find the vertex How to find the x- and y- intercepts.

Excellence Questions The Eagle Courier Company has a limit on the size of parcels it will deliver. The size of the parcel is calculated by finding.

Calculate: 1) The angle of the ladder to the ground.

A rectangular dog pen is constructed using a barn wall as one side and 60m of fencing for the other three sides. Find the dimensions of the pen that.

Check it out! : Multiplying Polynomials. Charlie is fencing in a rectangular area of his backyard for a garden, but he hasn’t yet decided on the.

4.4 Modeling and Optimization What you’ll learn about Examples from Mathematics Examples from Business and Industry Examples from Economics Modeling.

4.7 Applied Optimization Wed Jan 14

Quadratic Applications

Perimeter Of Shapes. 8cm 2cm 5cm 3cm A1 A2 16m 12m 10m 12cm 7cm.

QUADRATIC MODELS: BUILDING QUADRATIC FUNCTIONS

Lesson #3: Maximizing Area and Minimizing Perimeter

A Fencing Problem An Investigation Fencing Problem A farmer has 315m of fencing. He also has a field with a large wall. He uses the wall and the fencing.

4.7 Optimization Problems In this section, we will learn: How to solve problems involving maximization and minimization of factors. APPLICATIONS OF DIFFERENTIATION.

4.4. Optimization Optimization is one of the most useful applications of the derivative. It is the process of finding when something is at a maximum or.

Aim: Curve Sketching Do Now: Worksheet Aim: Curve Sketching.

Mathematical Models Constructing Functions. Suppose a farmer has 50 feet of fencing to build a rectangular corral. Express the rectangular area A he can.

Multiple Choice A carpenter wants to drill a hole that is just slightly larger than ¼ inch in diameter. Which of these is the smallest, but still greater.

Da Nang-11/2013 Natural Science Department – Duy Tan University Lecturer: Ho Xuan Binh Optimization Problems. In this section, we will learn: How to solve.

Optimization Problems Section 4.5. Find the dimensions of the rectangle with maximum area that can be inscribed in a semicircle of radius 10.

1. 2 Get a rectangular piece of paper and cut it diagonally as shown below. You will obtain two triangles with each triangle having half the area of the.

Teaching Techniques from Maria Aronne’s classroom.

Converse of Pythagoras Geometry Converse of Pythagoras In a triangle with sides a, b and c where c is the largest side, if a 2 +b 2 =c 2, then the triangle.

Optimization. First Derivative Test Method for finding maximum and minimum points on a function has many practical applications called Optimization -

Formulas: Perimeter of a rectangle: P = 2l + 2w Area of a rectangle : A = lw Perimeter of a square : P = 4s Area of a square: A = s 2 Circumference of.

REVIEW y = ax2 + bx + c is a parabola.  If a > 0, the parabola is oriented upward and the vertex is the minimum point of the function.  If a < 0, the.

Chapter 11 Maximum and minimum points and optimisation problems Learning objectives:  Understand what is meant by stationary point  Find maximum and.

Problem Solving: Geometry and Uniform Motion. 1. Find two supplementary angles such that the measure of the first angle is three times the measures of.

Sec 4.6: Applied Optimization EXAMPLE 1 An open-top box is to be made by cutting small congruent squares from the corners of a 12-in.-by-12-in. sheet of.

Optimization Problems 1.Identify the quantity you’re optimizing 2.Write an equation for that quantity 3.Identify any constraints, and use them to get the.

Sec 4.7: Optimization Problems EXAMPLE 1 An open-top box is to be made by cutting small congruent squares from the corners of a 12-in.-by-12-in. sheet.

STEPS IN SOLVING OPTIMIZATION PROBLEMS 1.Understand the Problem The first step is to read the problem carefully until it is clearly understood. Ask yourself:

T5.8 Max/min Finding Roots Topic 5 Modeling with Linear and Quadratic Functions 5.8.

2.6 Extreme Values of Functions

Optimization Problems. A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along.

Maximum Volume of a Box An Investigation Maximum volume of a box From a square piece of cardboard of side 20 cm small corners of side x are cut off.

Sect. 3-7 Optimization.

Solving word Problems.

Quadratic Word Problems

Revenue = (# of Calculators ) * ( price )

A Fencing Problem An Investigation.

Lesson 6: Optimizing Areas and Perimeters

2.4 Quadratic Models.

3.7 Optimization Problems

Find area L.O. calculating area and perimeter 2 cm 25 cm 30 cm² 50 cm²

MAXIMIZING AREA AND VOLUME

Area Of Shapes. 8cm 2cm 5cm 3cm A1 A2 16m 12m 10m 12cm 7cm.

Practical problems! Re-turfing the lawn?

3.7 Optimization Problems

Ch3/4 Lesson 8b Problem Solving Involving Max and Min

Optimization Problems

Area Of Shapes. 8cm 2cm 5cm 3cm A1 A2 16m 12m 10m 12cm 7cm.

3.3 Optimization Problems Day 1

A farmer has 100m of fencing to attach to a long wall, making a rectangular pen. What is the optimal width of this rectangle to give the pen the largest.

Introduction Jan 2006 ©RSH.

All About Shapes! Let’s Go!.

Cost of fencing, leveling and cementing

Power Point on Area- 5th Grade

Cost of fencing.

Sec 4.7: Optimization Problems

Polynomials 1 Tell me everything you can about this relationship:

Polynomials 1 Tell me everything you can about this relationship:

Circumference of circle Application

Copyright © Cengage Learning. All rights reserved.

Revenue = (# of Calculators ) * ( price )

Presentation transcript:

Sheep fencing problems Calculus

wall sheep fencing A farmer has a field in which there is a very long straight wall. The farmer also has 340 metres of fencing and he wishes to use this with the wall to fence of a rectangular area so that he can keep his sheep in and prevent them from wandering. The diagram below illustrates the situation. If x is the length of the short side of the rectangle shown, show that the area A which can be fenced is given by A= x(340 – 2x). Use calculus to find the dimensions of the field to ensure that the area will be a maximum.

Repeat the above calculations for a farmer in the same situation who has 246 metres of fencing.

A farmer has a field which contains two long walls which meet at right angles as shown. He also has 214 metres of fencing. Calculate the largest rectangular area which he can fence off. fencing wall sheep

Repeat the above situation for a farmer who has 157 metres of fencing.

fencing sheep A farmer has 259 metres of fencing. He wishes to fence off a rectangular area. Use calculus to find the maximum possible area he can fence off for his sheep.