Optimization Problems: Three Wall Rectangle Area Problems

Topics

  • Building a rectangular pen that utilizes a fixed amount of fencing and a pre-existing fourth wall
Steps: 
  • Draw a related picture and label with the given information
  • define your variables x and y are sides of the rectangle
    • F = 2x+y or F= 2y +x
  • Define your limitations on the variables 
  • Write one of the dimensions of the rectangle in terms of the given fence F and either x or y
  • Build an area function in terms of a single variable
  • Find the first and second derivative of the area function
    • The first derivative will allow you to find the location of potential extremes 
    • The first derivative will allow you to find the ROC of the area 
    • The second derivative should be negative at all of your critical values of x (this means that one of those critical values is your local maximum)
  • Sketch a graph of the area function 
    • only include quadrant one values for the feasible graph
  • Two of your critical values will be the x intercepts on this feasible region
  • The last critical value will be the root of the first derivative within the feasible region
Links and Resources
Polygon Resources
Optimize a rectangle formed by a parabola and the x axis 
This is the solution to a quiz originally given on 1-24-20
Video: Connection between given constraints, Rectangle Area model, and the derivative of a Rectangle Area Model