An escape game requires that players solve various puzzles to obtain objects that will aid them in escaping. In one such puzzle, players are given an array of integers and a set of rules to follow in order. Here are the instructions given to the player " given an array of integer values, maximize the points earned using the following method: a. Choose a value v delete all elements of that value and add their sum to the points.
b. Delete all elements equal to v+1 or v-1 for no points.
c. Repeat steps 1 and 2 until there are no more elements in the array.

Required:
Calculate the maximum number of points that can be achieved by following the above rules for an array of the values.

The volume v and paper surface area a of a conical paper cup are given by where r is the radius of the base of the cone and h is the height of the cone. a. by eliminating h, obtain the expression for a as a function of r and v. b. create a user-de ned function that accepts r as the only argument and computes a for a given value of v. declare v to be global within the function. c. for v ! 10 in.3 , use the function with the fminbnd function to compute the value of r that minimizes the area a. what is the corresponding value of the height h? investigate the sensitivity of the solution by plotting v versus r. how much can r vary about its optimal value before the area increases 10 percent above its minimum value?