Optimization: In each situation, set up and solve a global extrema problem that solves the given real- world optimization problem. (a) Alina needs to make a flyer for her band's concert. The flyer must contain 20 square inches of printed material and for design purposes should have side margins of 1 inch and top and bottom margins of 2 inches. What size paper should Alina use in order to use the least amount of paper per flyer as possible? (b) Your company produces cylindrical metal oil drums that must each hold 40 cubic feet of oil. How should the oil drums be constructed so that they use as little metal as possible? Can they be constructed to use as much metal as possible? C.) An airplane leaves Chicago at noon and travels south at 500 miles per hour. Another airplane is travelling east towards Chicago at 650 miles per hour and arrives at 2:00 p.m.. When were these two airplanes closest to each other, and how far apart were they at that time? (d) A steam pipe must be buried underground to reach from one corner of a rectangular parking lot to the diagonally opposite corner. The dimensions of the parking lot are 500 feet by 800 feet. It costs 5 dollars per foot to lay steam pipe under the pavement but only 3 dollars per foot to lay the pipe along one of the long edges of the parking lot. Because of nearby sidewalks, the pipe cannot be laid along the 500-foot sides of the parking lot. How should the steam pipe be buried so as to cost as little as possible