Three alternative designs have been created by engineer for a new machine that inspects solar power photovoltaic cells for home use. The costs for the three deigns (where x is the annual production rate follow: a) Management is interested in the production interval of 0-150,000 cells per year. Mathematically determine the production volume over which each design (A or B or C) would be chosen. b) Depict your solution from part (a) graphically, clearly labeling your axes and including a title for the graph, so that management can easily see the following: i. Accurate total cost lines for each alternative (show line, slopes, and line equations). ii. Any relevant breakeven or crossover point' in. Ranges of annual production where each alternative is preferred. c) Our decision rule is to minimize total cost across the range of output. How would your analysis approach change if some alternative produced an ethical dilemma? Describe your thinking