A hearing aid clinic is trying to determine how many batteries to purchase. The more batteries the clinic purchases the cheaper the batteries are. However, storing the batteries costs money (in the form of renting space). The cost of ordering x boxes of batteries is given by the function C(x)=21x21ln(x). The cost of storing x boxes of batteries is given by the equation S(x)=0.11(x50)2. a) Write an equation that models the total cost of purchasing and storing x boxes of batteries. Total cost: dollars b) Write an equation that models the cost per box of purchasing and storing x boxes of batteries. Cost per box: dollars c) How many boxes of batteries should the clinic order in order to minimize the cost per box? Do NOT round your answer. HINT: The equation x22121ln(x)+0.11x20.112500=0 has solution x=44.351. Boxes: 2121/x+0.22(x50)(21x21ln(x)+0.11(x50)2)/x2 d) At what price should the clinic sell a box of batteries to ensure that the clinic earns a profit of 30 dollars per box? Price per box dollars