Question

MTH 261 applied calculus

3. (a) You are given an unlimited amount of land to make a rectangular vegetable garden by city of Alexandria. But it must be fenced at your expense. Because of your frequent travel on the job, you decided to join with 2 of your friends (total participant 3 including you) for the project. Hence the plot to be divided into three sections and fenced also for each of the participant. based on the cost of fencing, you decided to buy 400 ft of fencing. What is the square footage of the LARGEST garden that you can grab? Verify that it is indeed, the LARGEST plot. (15 points) (b) During Gulf oil crisis, the EPA biologists estimated that the radius of the CIRCULAR {Area =T * (radius) 2} oil patch was increasing at a rate of 5 ft. /sec. They would like to estimate the rate of marine life coverage (in ft2/sec) as a function of the radius. They asked your help (as a mathematician in the group) to provide a plot for the group. Plot that graph. (10 points)