Problem 3 (Spreadsheet Construction): A coin collector has to sell a rare quarter in near-mint condition from the year 1899 . She's trying to decide the price. If she prices the coin too high, it'll take a long time to sell but she'll get a high price. If she prices the coin too low, it'll sell almost immediately but she won't get much money for it. Based on her understanding of the rare coin market, the following equation tells her how many days she'll have to wait for the coin to sell: delay=0.008price1.15 Her utility for selling the coin depends both on the delay and the price she gets as follows: utility=0.97delayprice0.97 Although she'd like to maximize her utility from selling the coin, she realizes that if she charges a price too low, not only will she not get a good price, but it will also devalue the rest of her collection. If she charges any less than 80% of the face value estimate of $1162, the value of all of her collection's coins will drop. This is unacceptable. She also has a strict timeline for the money. She has to make sure the coin sells before her rent is due in 27 days. Construct a spreadsheet for her problem so that she'll be able to use your spreadsheet to properly set the price to maximize her utility while making sure the rent is paid on time and she doesn't devalue her remaining coins. The influence diagram for this problem is shown in the next page. \begin{tabular}{|l|} \hline Price \\ \hline$1090 \\ \hline$1100 \\ \hline$1110 \\ \hline$1120 \\ \hline$1130 \\ \hline$1140 \\ \hline$1150 \\ \hline$1160 \\ \hline$1170 \\ \hline$1180 \\ \hline$1190 \\ \hline$1200 \\ \hline \end{tabular} Question 3 (Spreadsheet Construction): Of the prices shown in the table, which one gives the highest utility without violating any constraints? Problem 3 (Spreadsheet Construction): Continue to look at increasingly higher prices in increments of $10 (just like the table of prices above). How much higher could her utility be if she could delay paying rent for 5 additional days? Hint: Include at least 2 digits after the decimal