. Question 9 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 O(x) = 4x + 12000x] + 6000 models their total inventory costs (in dollars) as a function of r 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. 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.) What is their minimum total inventory cost? $. Question 10 Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.01q' + 4q -22, where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing q pairs of sunglasses. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer. ) Answer: MP(q) B) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.) Answer: thousand pairs of sunglasses need to be sold. () What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.) Answer: thousand dollars of maximum profits can be expected.. Question 11 Suppose a company's revenue function is given by R(q) = -q* + 260q and its cost function is given by C(q) = 180 + 12q, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) MP(q) = B) How many items (in hundreds) need to be sold to maximize profits? Answer: hundred units must be sold. (Round to two decimal places.)