As a preliminary investigation for the release of a top-secret project, your company has asked you to determine the spring constants for a collection of reference springs. fortunately, the measurements have already been carried out and you have only to interpret them. recall that spring displacement is governed by hooke's law, f = -k x where x is the observed displacement and f is the corresponding required force. since it is experimentally easier to use mass instead of displacement, the data sets instead specify mass, related by f = m/1000 * g where m is mass in grams and g is acceleration due to gravity. thus the spring constant k may be determined from the experimental data as the slope of the line fitting displacement and force data. the data are recorded in the format [ m x ]; that is, the mass in the first column and the displacement observed in the second. 5 15.5 10 33.07 20 53.39 50 140.24 100 301.03 compose a function `fit_spring` which accepts an array of data in this format and returns the corresponding spring constant k. use g=9.81

1. the materials manager for a billiard ball maker must periodically place orders for resin, one of the raw materials used in producing billiard balls. she knows that manufacturing uses resin at a rate of 50 kilograms each day, and that it costs $.04 per day to carry a kilogram of resin in inventory. she also knows that the order costs for resin are $100 per order, and that the lead time for delivery is four (4) days.2. at what point should resin be reordered? a. 0 kilograms remainingb. 50 kilograms remainingc. 200 kilograms remainingd. 400 kilograms remaininge. 500 kilograms remaining3. if order size was 1,000 kilograms of resin, what would be the length of an order cycle? a. 0.05 daysb. 4 daysc. 16 daysd. 20 dayse. 50 days4. if the order size was 1,000 kilograms of resin, what would be the average inventory level? a. 50 kilogramsb. 200 kilogramsc. 500 kilogramsd. 800 kilogramse. 1,000 kilograms5. if the order size was 1,000 kilograms of resin, what would be the daily total inventory costs, excluding the cost of the resin? a. $5b. $10c. $20d. $25e. $40