Suppose we wanted to make change for purchases and wanted to use the least number of coins possible. Here is a greedy algorithm: for the change amount due, we always use the largest-face-value coin first. Assume we have only coins of quarters ($.25), twenties ($.20), and pennies ($.01). Assume the change is $.40: a. what would be the coins and their numbers obtained by the greedy algorithm above

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?