IE 335: Operations Research - Optimization Laboratory Report 1 Fall 2020 -Area Optimization Objectives: Optimize (minimize the perimeter of a fence that surrounds parking space with given surface area Background A rectangular parking space with surface area A has to be created along the strait road. The parking area will have a fence around its three sides (there is no need for a fence on the roadside). Your goal is to come up with such a width and length of the parking area that will minimize the perimeter of the fence. What should be the width and length of the area? The alternatives of the problem are identified by defining the width and length as continuous (algebraic) variables. Let W = width of the area in meters Let L = length of the area in meters Based on these definitions, the restrictions of the situation can be expressed verbally as: Length of the rectangle x Width of the rectangle Area of the rectangle Length of the rectangle + 2 x Width of the rectangle = Perimeter of the fence Width and length cannot be negative Tasks: 1. Read the problem carefully and draw a picture illustrating the situation 2. Identify the decision variable(s) in this problem. 3. Set up the objective function for the parking to optimize. 4. Identify the constraints the solution must satisfy 5. Reduce the formulas in the problem to one decision variable. 6. Solve the problem using basic calculus knowledge to find a. The domain of the objective function b. Find the critical point(s), and explain what indication the critical point of the function can tell c. Determine the absolute max and min of the objective function. d. Sketch the graph of the objective function e. Identify the optimal value(s) 7 Solve the problem in EXCEL by enumerating possible values of the decision variable(s) and finding the one that gives the maximum area, a. In this approach, you first have to fix a value of the problem constant A (Area) to a specific value. b. Provide an EXCEL graph of the objective function after numerating values to the decision variable. c Identify the optimal value(s) you find. IE 335: Operations Research - Optimization Laboratory Report 1 Fall 2020 -Area Optimization Objectives: Optimize (minimize the perimeter of a fence that surrounds parking space with given surface area Background A rectangular parking space with surface area A has to be created along the strait road. The parking area will have a fence around its three sides (there is no need for a fence on the roadside). Your goal is to come up with such a width and length of the parking area that will minimize the perimeter of the fence. What should be the width and length of the area? The alternatives of the problem are identified by defining the width and length as continuous (algebraic) variables. Let W = width of the area in meters Let L = length of the area in meters Based on these definitions, the restrictions of the situation can be expressed verbally as: Length of the rectangle x Width of the rectangle Area of the rectangle Length of the rectangle + 2 x Width of the rectangle = Perimeter of the fence Width and length cannot be negative Tasks: 1. Read the problem carefully and draw a picture illustrating the situation 2. Identify the decision variable(s) in this problem. 3. Set up the objective function for the parking to optimize. 4. Identify the constraints the solution must satisfy 5. Reduce the formulas in the problem to one decision variable. 6. Solve the problem using basic calculus knowledge to find a. The domain of the objective function b. Find the critical point(s), and explain what indication the critical point of the function can tell c. Determine the absolute max and min of the objective function. d. Sketch the graph of the objective function e. Identify the optimal value(s) 7 Solve the problem in EXCEL by enumerating possible values of the decision variable(s) and finding the one that gives the maximum area, a. In this approach, you first have to fix a value of the problem constant A (Area) to a specific value. b. Provide an EXCEL graph of the objective function after numerating values to the decision variable. c Identify the optimal value(s) you find