On June 1, Edward visited a bicycle sales and service center. Edward spotted a used bike he liked and was told by the dealer that he could have the bike for $100 cash. Since Edward needed a few days to get the money, Edward got a signed, written statement by the dealer that Edward could buy the bike for $100 at any time on or before June 15. On June 10, Edward came to the dealer with the money, but the bike had been sold to another customer. Was the dealer under any obligation to Edward to keep this offer open until June 15? Give legal reasoning for your answer.