Please show work on Problems 3, 4, and 5. Elaborations are much appreciated!

Decision Tables and Decision Trees Problem 3. Assume that the owners of a video store are planning to implement a "preferred customer" program to encourage repeat business. In this program, customers get bonus points for each rental that can later be used towards rental fees. The description of the program is as follows: The proposed system will calculate bonus points based on the rental activity of a customer at the end of each month. - The customer will be awarded a base rate of 50 bonus points per rental made during a one month period. - If a rental occurs on a Saturday or a Sunday (weekend bonus), the number of bonus points awarded for the rental are doubled. - If a rental occurs on a Tuesday (slow day bonus), the multiplication factor is 1.5 . - Normal day rentals (made on all other days except Tuesday, Saturday or Sunday) are rewarded with no special incentive (i.e., a multiplier of 1). - New movie rentals are awarded a further premium of 1.25 times the bonus points that would accrue otherwise. To encourage timely payment of dues, the owners reward customers that pay their bills on time. - If, at the end of the month, there is less than $10 in the balance due from the customer, the bonus points awarded during the month are doubled. - If there is zero balance, the bonus points are tripled. - No bonus points are awarded during a month in which the end-of-month- balance is greater than $10. That is, if a customer earns 500 bonus points from a month's rental activity, but the balance due is more than $10, then zero bonus points are awarded for that month. Note: When in doubt, make a reasonable assumption, but clearly state it. Develop a decision table and decision tree for the video store's new award policy, so that the policy becomes easier to grasp visually and hence easier to explain. Problem 4. Consider the following information on a decision process used within an organization to grant salesperson commissions: If fewer than 400 units are sold, the salesperson's commission is 1% of total sales. If between 400 and 499 units are sold, the salesperson's commission is 2% of total sales. If 500 or more units are sold and the salesperson has been with the company for more than one year, the salesperson's commission is 4% of total sales. If 500 or more units are sold and the salesperson has been in the company for one year or less, his or her commission is 3% of total sales. In addition to the above commission scheme, an additional commission of 0.5% of total sales is added if more than 80% of the sales have been collected by the salesperson. Draw a decision table representing the above information. Convert the table to an optimal decision tree from the standpoint of the mumber of inputs observed to make a decision. Problem 5. Convert the decision table below into a condensed table by eliminating all redundant information. Draw an optimal decision tree using the condensed table. Calculate the expected cost associated with the tree under the following assumptions: Cost of A=$2 Cost of B=$1 Cost of C=$5 Cost of D=$3 P(A is True )=0.7 P(B is True )=0.3 P(C is True )=0.5 P(D is True )=0.8 Problem 3. Consider a simple coding scheme for the inputs are Rental Type (W, S, O) for Weekend, Slow and Other New Movie (Y,N) Balance (H,M,L) Then solve as discussed in class. Problem 4. Coding Scheme Units Sold (H,M,L) Age with Company (H,L) Collections (Y,N) Problem 5 Easy