@ Question 1 v For the given cost function C(z) = 57600 4 700z + z* find: a) The cost at the production level 1700 | b) The average cost at the production level 1700 | c) The marginal cost at the production level 1700 ' d) The production level that will minimize the average cost ' e) The minimal average cost @ Question 2 v For the given cost function C(z) = 250/ + find T 166375 a) The cost at the production level 1050 | b) The average cost at the production level 1050 ' ) The marginal cost at the production level 1050' d) The production level that will minimize the average cost. ' e) The minimal average cost. ' Give answers to at least 3 decimal places. @ Question 5 v A manufacturer has been selling 1650 television sets a week at 5540 each. A market survey indicates that for each $12 rebate offered to a buyer, the number of sets sold will increase by 120 per week. a) Find the demand function p(z), where z is the number of the television sets sold per week. p(z) = | b) How large rebate should the company offer to a buyer, in order to maximize its revenue? | c) If the weekly cost function is 148500 + 180z, how should it set the size of the rebate to maximize its profit? : | . Question 7 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(z) = 4z + 32000z " + 16000 models their total inventory costs (in dollars) as a function of x 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? $ 0 @ Question 9 v Suppose the Sunglasses Hut Company has a profit function given by P(g) = (].U'3q2 + 6g 44, where g 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 g pairs of sunglasses. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) Answer: M P(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. C) 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 10 v Suppose a company's revenue function is given by R(q) = q3 + 2909'2 and its cost function is given by C(q) = 190 + 18g, where g is hundreds of units sold/produced, while R(g) 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.) &1/2p Question 2 v Next question o Get a similar question You can retry this question below 22 For the given cost function C(z) = 250/ + find s (=) V= 56375 a) The cost at the production level 1050 | 8124.194 X b) The average cost at the production level 1050 | 7.737 X ) The marginal cost at the preduction level 1050 | 3.870 ~/| o d) The production level that will minimize the average cost. ' 75625 ~/| o e) The minimal average cost. 1.363 v'\\' o Give answers to at least 3 decimal places. Question 8 v Next question o Get a similar question You can retry this question below 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(z) = 4z + 32000z + 16000 models their total inventory costs (in dollars) as a function of x 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.) ' 89 J' o What is their minimum total inventory cost? 1641555 X