The Flintstones Mr. Slate from the Bedrock Quarrel and Gravel Company decides in is time to clean house, so he puts up several items up for bid. He decides to use the sealed bid method and open the process to Fred and Wilma Flintstone and Barney and Betty Rubble. Each party places a bid on each of the items. The table below shows the bids on each item. Item 1 Item 2 Item 3 Item 4 Item 5 Fred $75 $30 $60 $20 $45 Wilma $58 $65 $30 $70 $35 Barney $25 $70 $55 $80 $50 Betty $45 $80 $40 $55 $45 Based on the information in the chart determine which person gets which item along with any cash payouts. Show how you reached your decision and explain how it is an equitable solution to the problem One method of dividing something among three or more people is the Lone Divider Method. The method for N parties proceeds as follows: 1. The divider divides the item into N pieces, which the divider deems to be equal in value. Each piece is labeled 2. Each of the choosers will separately list which pieces they deem to be their fair share. This is their declaration or bid. 3. The lists are examined. Two possibilities exist: a) If it is possible to give each party a piece they declared, then we give it to them. The divider gets the remaining piece. b) if two or more parties want the same piece and no other pieces, then the divider gets the uncontested piece. The rest of the pieces are combined, and we repeat the entire process with the remaining parties. If only two parties are left, they can use the "I cut you choose" method. Sealed Bids Method This method is to help divide a set of items that cannot be divided into pieces (house, car, furniture, etc.). Each party secretly lists a value they believe each item is worth, also known as their sealed bid. Each party determines what a fair share is to them by dividing the total value they placed on all items by the number of parties. The sealed bids are collected and the highest bidder on each of the items will get that item. The value of all items received is totaled for each party If a player received more than their fair share, they pay the difference to a holding pile Any player who received less than their fair share is paid the difference from the holding pile. Any surplus or leftover money in the holding pile is paid evenly among the parties. Example: Two siblings, John and Susan, need to split up several items amongst themselves and decide to do so using sealed bids The two place bids on the three items and count them up. This will also determine what each of them values a fair share to be. John $20 $30 $50 $40 $80 $90 $150 $160 $150 $160 $75 $80 2 . . Susan Item 1 Item 2 Item 3 Total Fair Share Fair Share $150 $75 $160 2 $80 2 . The highest bidder for each item will receive that item. Therefore, John gets item 2, and Susan gets items 1 and 3. Susan received items 1 and 3, but the total value of the two items is $30+$90=$120. This is more than a fair share to Susan, and she must pay the difference of $120-$80=$40 into a holding pile. John only received item 2 which is worth less than a fair share to him. John will receive money from the holding pile to make up for the difference. John will receive $75-$50-$25 from the holding pile. The $15 remaining in the holding pile is then distributed evenly between the two. Both siblings receive $7.50 from the holding pile. In the end, John received item 2 and received$32.50. Susan received items 1 and 3 and paid $32.50 to John