2) Assume that your widget manufacturing company has a total annual demand of N widgets per year evenly distributed across the year. Each widget cost $b dollars in material and manufacturing costs to make. Every time you do a production run to make some widgets, you incur a set-up cost of P dollars. Any widgets awaiting sale must be stored and thus incur an average storage fee of c dollars per widget per year. Let x be the size of each production run (i.e., x is the number of widgets per production run). a) Write a cost function C(x) and explain each term in the equation and how it was determined. b) Write down any constraints on the allowable values of x. c) Determine a formula for the value of x that minimizes total annual cost. Show all of your work. d) Prove that your formula actually corresponds to the global minimum cost. e) Write down a formula for the number of production runs per year as a function of x.