Table 1. Candies available for purchase, dimensions, and cost per candy Candy Shape Size Cost per candy Spheres Radius = 10 mm 7 cents Radius = 15 mm 11 cents Radius = 20 mm 13 cents Cubes Length = 10 mm 6 cents Length = 12 mm 9 cents Length = 17 mm 12 cents Cones Length = 17 mm Radius = 7 mm 7 cents Length = 19 mm Radius = 7 mm 10 cents Length = 20 mm Radius = 9 mm 12 cents Cylinders Length = 14 mm Radius = 7 mm 5 cents Length = 17 mm Radius = 7 mm 7 cents Length = 17 mm Radius = 9 mm 10 cents You expect to sell each candy at a cost of 25 cents each (independent of their size). Your team also needs to acquire a machine to dispense the candy. There are two machines available. The shape of both machines are shown in Figures 1 and 2, with dimensions indicated in Tables 3 and 4. Machine 1 costs $275. Machine 2 costs $320. Fall 2017 Dr. Lizzie Santiago It is known that when packing candies in a container, less than 100% of the containers total volume is occupied by the candies (the remainder is lost to air pockets between the candies). Table 2 gives the random packing densities for the various candy shapes. Table 2. Random packing densities of candy shapes Shape Random Packing Density Sphere 0.64 Cube 0.78 Cone 0.67 Cylinder 0.72 You have found the results of a statistical analysis for the purchase of candy in a typical college. These results indicate that out of every 250 people who enter the lobby 3 people buy a candy. Assume that each person buys one candy. A recent survey shows that 6488 people walk through the ESB lobby per day. One final concern is that the machine must be refilled when it reaches 20% of its total capacity. There is a $25 service fee to have a machine refilled. Table 3. Dimensions of machine 1 Stage Properties Stage 1 Cylinder with Diameter= 0.25 m Height = 1 m Stage 2 Cone with Diameter= 0.25 m Height= 0. 25 m Table 4. Dimensions of machine 2 Stage Properties Stage 1 Cylinder with Diameter= 0.2 m Height = 1.2 m Stage 2 Cylinder with Diameter= 0.1 m Height= 0. 4 m To decide whether this venture is profitable, you need to calculate the following information: 1. What is the total number of candies that can be placed in each machine? Use an fprintf command to display your answer. 2. How often must each machine be refilled? Use an fprintf command to display your answer. Stage 1 Stage 2 Stage 1 Stage 2 Figure 1. Machine 1 Figure 2. Machine 2 Fall 2017 Dr. Lizzie Santiago 3. How much would each refill cost (including both the added candies, and the service fee)? Use an fprintf command to display your answer. 4. What would be the number of refills at the end at the first year? Use an fprintf command to display your answer. 5. What would be the profit at the end of the first year? Be sure to take the initial cost of filling the machine into account. Use an fprintf command to display your answer. 6. What would be the total profit (cumulative) at the end of the second year? Use an fprintf command to display your answer. 7. For each candy, create two separate tables to present your final answers (to questions 13). Your output should follow the following format (example on how it will look for spheres): Machine Type/Candy Refill Frequency (days/refill) Cost per Refill Number Refills First Year Machine 1 Spheres r10 Machine 1-Spheres r15 Machine 1-Spheres r20 Machine 2 Spheres r10 Machine 2-Spheres r15 Machine 2-Spheres r20 Machine Type/Candy First Year Profit Second Year, Cumulative Profit Machine 1 Spheres r10 Machine 1-Spheres r15 8. The Dean of the college is requesting information on the number of candies inside the machine, and is asking you to create a program that asks the user to enter the height of candies in the candy machine, and the program displays the total number of candies left in the machine (using an fprintf command) NB: Figure 1 (stage 1 cylinder)(stage 2 cone) Figure 2 (stage 1 cylinder)(stage 2 cylinder)