Using Matlab to solve
You have a job working for construction company that builds fenced dog runs. These dog runs are rectangular where one of the short ends is either replaced by semicircle or half of a hexagon, see figures below. The cost of the run is a function of the total length of fence on its perimeter versus the amount of square feet contained within the shape. So, the objective of the company is to minimize fence costs and maximize enclosed area for given overall lengths and widths of the dog run. The problem is that many customers have a space that constrains one dimension, width, W or the length, L, but the other one is able to vary within a range. L L w w Therefore, your boss wants you to develop a MATLAB program that will produce a table of length, width, enclosed area and fence perimeter length when one of the dimensions is constrained and the other is allowed to change in 3-foot increments from bottom to top of the range for either the semicircular or hexagon ends. a) (10 points) Develop a MATLAB M file that will calculate enclosed area and fence perimeter when the width is equal to 12 feet and the length is equal to 36 feet. b) (5 points) Develop a MATLAB M file that will allow inputs for length and width and then identify which is to be held constant and the range that the other is allowed to very between and to allow identification of which shape of dog run is preferred. Output for this will be in a tabular format giving the following information: fixed dimension, variable dimension and the resulting fence perimeter length and enclosed area for each of those variables. c) (5 points) Use the information from part B above to develop a plot of the same data BONUS: (5 points) If the end of the rectangle were to be changed from either a hemisphere or hexagon to an equilateral triangle (W is the length of each side), what would be the percentage loss or gain of run area or fence length for the same length, L, and width, W, as in part a? You have a job working for construction company that builds fenced dog runs. These dog runs are rectangular where one of the short ends is either replaced by semicircle or half of a hexagon, see figures below. The cost of the run is a function of the total length of fence on its perimeter versus the amount of square feet contained within the shape. So, the objective of the company is to minimize fence costs and maximize enclosed area for given overall lengths and widths of the dog run. The problem is that many customers have a space that constrains one dimension, width, W or the length, L, but the other one is able to vary within a range. L L w w Therefore, your boss wants you to develop a MATLAB program that will produce a table of length, width, enclosed area and fence perimeter length when one of the dimensions is constrained and the other is allowed to change in 3-foot increments from bottom to top of the range for either the semicircular or hexagon ends. a) (10 points) Develop a MATLAB M file that will calculate enclosed area and fence perimeter when the width is equal to 12 feet and the length is equal to 36 feet. b) (5 points) Develop a MATLAB M file that will allow inputs for length and width and then identify which is to be held constant and the range that the other is allowed to very between and to allow identification of which shape of dog run is preferred. Output for this will be in a tabular format giving the following information: fixed dimension, variable dimension and the resulting fence perimeter length and enclosed area for each of those variables. c) (5 points) Use the information from part B above to develop a plot of the same data BONUS: (5 points) If the end of the rectangle were to be changed from either a hemisphere or hexagon to an equilateral triangle (W is the length of each side), what would be the percentage loss or gain of run area or fence length for the same length, L, and width, W, as in part a
