1. Roger Clark obtains long-stem roses from Freds Flowers each Friday for sale to the public. Fred generally sells Roger flowers that, if left over the weekend, would likely be unsalable the next week. Hence, he is willing to give Roger a good price on his remaining long-stem roses and to take back any roses that are not sold over the weekend and give Roger partial credit for them. Roses are sold to Roger in quantities or units of one dozen each and at a price of $10 per dozen. Roger sells the roses for $15 per dozen, and any remaining unsold over the weekend can be returned to Fred at a credit of $8 per dozen. Although the number of roses remaining to be sold at the end of the week varies, Fred is willing to let Roger have as many as six dozen each weekend and supply him with fresh flowers at the same price if Roger desires more than the quantity of old roses that Fred has. Characterize this decision problem both in terms of the various states of nature (demands) and in terms of the various acts (supplies) open to Roger. Construct the payoff and loss matrices for this problem.