45) For the given cost function C(x) = 62500 + 500x + x², First, find the average cost function. Use it to find: a) The production level that will minimize the average cost x = ________ b) The minimal average cost $_____

46) A farmer finds that if she plants 90 trees per acre, each tree will yield 45 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 2 bushels. How many trees should she plant per acre to maximize her harvest? ________ trees Give your answer rounded to the nearest whole number.

47) Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and then sell it to customers in their store. The function C(x) = 3.5x + 30000x^-1 + 12000 models their total inventory costs (in dollars) as a function of xx the lot size for each of their orders from the supplier. The inventory costs include such things as purchasing, processing, shipping, and storing the equipment. (a) What lot size should Glorious Gadgets order to minimize their total inventory costs? (NOTE: your answer must be the whole number that corresponds to the lowest cost.) (b) What is their minimum total inventory cost?