Question

Use Knaster's Method of Sealed Bids to determine the compensation. The people and items involved are given in this table. Items Aberforth Bellatrix Cornelius Dudley Wardrobe $320.00 $240.00 $300.00 $260.00 Tapestry $220.00 $140.00 $200.00

Answer 1

The compensation determined using Knaster's Method of Sealed Bids for the items involving Aberforth, Bellatrix, and Cornelius is as follows:

• Aberforth: $270.00
• Bellatrix: $126.67
• Cornelius: $166.67

Step-by-step explanation:

Knaster's Method of Sealed Bids involves a fair and efficient way to determine compensation in a sealed bidding scenario. In this case, the compensation for each participant (Aberforth, Bellatrix, and Cornelius) is calculated based on their bids for the respective items (Wardrobe and Tapestry).

Firstly, for Aberforth, the average of the bids on both items is calculated:
`\((($320.00 + $220.00))/(2) = $270.00\).` This average serves as the fair compensation for Aberforth.

Similarly, for Bellatrix, the average of her bids on both items is calculated:
`\((($240.00 + $140.00))/(2) = $190.00\)`. However, since this is a sealed bidding scenario, Knaster's Method adjusts the compensation to two-thirds of the average bid, resulting in
`\(2/3 * $190.00 = $126.67\)` for Bellatrix.

For Cornelius, the average of his bids on both items is calculated:
`\((($300.00 + $200.00))/(2) = $250.00\).`. Again, applying Knaster's Method, Cornelius's compensation is adjusted to two-thirds of the average bid, resulting in
`\(2/3 * $250.00 = $166.67\).`

In conclusion, the compensation for each participant is determined by averaging their bids on the items and applying Knaster's Method adjustment, ensuring a fair and balanced outcome in the sealed bidding process.