$2.$ The table below shows the bids from three buyers and the offers from three sellers in a centralized electricity market. Apply the High$-$Low Matching mechanism as described in the lecture to determine which transactions will be executed. Then, calculate the execution price for each matched pair $($as the average of the buyer's bid and the seller's offer$),$ and finally compute the overall weighted average execution price for all successful trades.

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|$l$|$l$|\}$

$\backslash$hline Buyer ID & Bid Price $(\backslash$$$/$MWh$)$ & Bid Quantity $($MWh$)$ & Seller ID & Offer price $(\backslash$$$/$MWh$)$ & Bid Quantity $($MWh$)\backslash \backslash$

$\backslash$hline $1$ & $55$ & $100$ & $1$ & $45$ & $60\backslash \backslash$

$\backslash$hline $2$ & $52$ & $80$ & $2$ & $47$ & $80\backslash \backslash$

$\backslash$hline $3$ & $50$ & $60$ & $3$ & $50$ & $100\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$