Tidus Skis has determined from sales records that their profit is given by P(x) =500x -2x , 0S * $ 250, where x is the number of pairs of skis manufactured each week and P(x) is the profit in dollars. a. Determine P'(x) and interpret it. b. Compute P'(50) and P'(200) and interpret the results.Atlas Air has determined that the cost of maintenance of operating x airplanes is given by (\\*) =1.15 +2.05 In( +1), * 2 0 , where the cost ((x) is in hundreds of thousands of dollars. (a) Evaluate C(10) and interpret. Round to two decimal places. (b) Compute the average rate of change for x=2 and Ax =2 and interpret.Atlas Air has determined that the cost of maintenance of operating x airplanes is given by C(x) = 1.15 +2.05 In(x +1), x 2 0 , where the cost ((x) is in hundreds of thousands of dollars. (a) Evaluate C(10) and interpret. Round to two decimal places. Compute the average rate of change for x=2 and Ax =2 and interpTidus Skis has determined from sales records that their profit is given by P(x) =500x -2x , 0S * $ 230, where x is the number of pairs of skis manufactured each week and P(x) is the profit in dollars. a. Determine P'(x) and interpret it. b. Compute P'(50) and P'(200) and interpret the results.Dixie Import-Export is the sole agent for the Excalibur250-cc motorcycle. Management estimates that the demand for these motorcycles is 10,000 per year and that they will sell at a uniform rate throughout the year. The cost incurred in ordering each shipment of motorcycles is $10,000, and the cost per year of storing each motorcycle is $200. Dixie's management faces the following problem: Ordering too many motorcycles at one time ties up valuable storage space and increases the storage cost. On the other hand, placing orders too frequently increases the ordering costs. How large should each order be, and how often should orders be placed, to minimize ordering and storage costs