In the Fractional Knapsack Problem, you are allowed to take f of each object, where f is some r number between 0 and 1. Your goal is to pick the objects that maximize the total value of yo knapsack, with the condition that the chosen objects weigh at most 10 pounds. Determine the maximum total value of your knapsack.

There are a set of courses, each of them requiring a set of disjoint time intervals. For example, a course could require the time from 9am to 11am and 2pm to 3pm and 4pm to 5pm. You want to know, given a number K, if it’s possible to take at least K courses. You can only take one course at any single point in time (i.e. any two courses you choose can’t overlap). Show that the problem is NP-complete, which means that choosing courses is indeed a difficult thing in our life. Use a reduction from the Independent set problem.

Using pyhton coding to solve: Suppose the Great Frederick Fair wants to update its ticketing software. They need you to write a program to handle the price calculations, using the rules*: ● The basic price of a ticket is $40. Senior citizens (age >= 65) get a 50% discount. Children under 6 are free (100% discount). For residents of Frederick County, the basic price is $35; the same discounts still apply. So the individual ticket prices range from $0 to $40. ● . Your program should request age and county name from the user. The age will be entered as an integer and the county name as a string. Before calculating the price, confirm that the user's age is valid - not negative and not more than 110. If it is not, give a message and do not do the price calculation. Also, the county name should not be case sensitive - for example, Frederick, frederick, and FREDERICK should all be acceptable. Your program should then calculate and print out the ticket price, using the appropriate…