Inventory Control A company anticipates there will be a demand for 20,000 copies of a certain book during the next year/. It costs the company $0.50 to store a book for 1 year. Each time it must print additional books, it costs $200 to set up the equipment. NOTE: We assume that the demand is uniform. Let . = number of books printed during each printing run . y = number of printing runs Use this information to answer questions 9-19 below. Question 9 0.4 pts Use the Inventory Control information above to answer this question. The total setup cost for the year is y. 200Use the Inventory Control information above to answer this question. Since we assume the demand is uniform, the number of books in storage between printing runs will decrease from _ to The average number in storage for each day is Question 11 0.5 pts Use the Inventory Control information above to answer this question. Since it costs $0.50 to store a book for one year, the total storage cost is Enter your answer as a decimal. 0.5Use the Inventory Control information above to answer this question. The total cost is the sum of the setup cost and storage cost, so C = 200 v yt 0.5 Question 13 0.4 pts Use the Inventory Control information above to answer this question. In order to write the total cost as a function of one variable, we must find a relationship between : and y. Since the company prints @ books in each of the y printing runs, the total number of books printed is ay, so we must have Cy = We can use this to express y as a function of c. 20,000Use the Inventory Control information above to answer this question. Since a: is the number of bool-ts printed in each printing runr 3 must satisfy 1 E a: :1: In other words a: is in the closed interval [11, b]1 where o = l and b 2 Question 15 {15 pts Use the Inventory Control information above to answer this question. Using the calculations above we can express the total cost C(31) as a function of or, with the restriction on a: given in the previous problem. Fincl the critical number of C(31) by solving C'[a:} = . MUTE: Because of the restriction on or, there is exactly one critical number c. Use the Inventory Control information above to answer this question. There is only one critical number c in the interval, and the cost function C(a) is continuous. Since C' (c) [ Select ] and C" (c) [ Select ] . we can use the [ Select ] to conclude that O(c) is the [ Select ] of the cost function on the interval I. Question 17 0.5 pts Use the Inventory Control information above to answer this question. How many books should be produced during each printing run to minimize total cost? booksUse the Inventory Control information above to answer this question. How many printing runs should be done? printing runs Question 19 0.5 Use the Inventory Control information above to answer this question. What is the minimum total cost? $