c. Use the constraints to eliminate all variables except for the point of intersection B. d. Find the first derivative of the objective function and set it equal to zero. e. By hand, find the zeros of the function. Check zeros and endpoint values to find the maximums of the objective function. f. Use this finding to extrapolate why the smaller circles should be equal to maximize the area of the arbelos. ir'ou have been tasked with designing a double carport in the shape of a halfcylinder. The top of the front opening needs to be in the shape of an arbelos. An arbelos is a shape formed by three mutuallv tangent semicircles. It is the region inside the largest semicircle and outside the two smaller semicircles. See the design below [blue shaded area}. We have two separate parts ofour design. In the first part, we want to show the maximized area ofthe arbelos is when the two smaller semicircles are the same size. Next, we want to minimize the carport cost considering the entire halfcylinder volume is 9,000 cubic feet. A B c 1. First we need to show the two smaller halfcircles ofthe arbelos need to be the same size to maximize the area ofthe arbelos {blue-shaded region]. Another way to look at it is the distance AB = BC. a. Suppose the diameter ofthe largest semicircle AC in the arbelos has a diameter of 1 unit. Identify the objective function in terms of points A, B. and C. Hint: The objective function is to maximize the area of the arbelos. This can be accomplished by taking the area ofthe larger CA semicircle (radius = T) and subtracting the areas ofthe two smaller semicircles (radius = 311 (33 and i 2 2 b. Identify the constraints and let A = D. This means (I: 1