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Scenario: Vladimir and Alphonso Are Collectors of Toy Story Figurines 12 \frac{1}{2}

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Scenario: Vladimir and Alphonso are collectors of Toy Story figurines. Each has six dollar bills to spend on three figurines-Sheriff Woody, Buzz Lightyear, and Jessie-that are put up for auction where Vlad and Alph are the only bidders. They simultaneously and independently write down their bids, in whole numbers adding up to $6, for the three figurines and give them to the auctioneer. Whoever wrote the higher number for a figurine wins it. For example, if Vlad bids ($3, $1, $2) , meaning $3 for Sheriff Woody, $1 for Buzz Lightyear, and $2 for Jessie, and Alph bids ($2, $3, $1) , then Vlad wins Sheriff Woody and Jessie, while Alph wins Buzz Lightyear. If there is a tie, then a fair coin is flipped to determine the winner so that each bidder has 50 percent chance of winning a figurine. Vlad and Alph consider this case as "winning" a 12 \frac{1}{2} figurine. Vlad and Alph care only about how many more, or less, figurines they win compared to the other.
-Refer to the scenario above.If Vlad bid ($2,$2,$2) ,then he can win at least ________,no matter what Alph does.


Definitions:

Cost Center

A department or unit within an organization that does not directly contribute to profit but incurs costs for its operation.

Responsibility Center

Any business segment whose manager has control over costs, revenues, or investments in operating assets.

Queue Time

The duration a product or job order spends waiting to be processed, not including the time actually taken to complete the task.

Non-value-added Time

Time during production that does not directly contribute to the final value of the product, such as waiting times or transportation of goods.

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