A group of Physicians must build an addition to their existing private clinic. They are considering three different sized additions; a small, a medium and a large addition. If the medical demand is high, they would realize a net profit of $$100,000$ with a large addition, a net profit of $$40,000$ with a medium addition and a net profit of $$10,000$ with a small addition. Ifhe medical demand is low they would realize a net loss of $$40,000$ with the large addition, a net loss of $$10,000$ with the medium addition and a net profit of $$5,000$ with the small addition. The Physicians were also able to assign utility preference values to each of the potential payoffs they could encounter. Utility of $$100,000$ is $1\mathrm{.}0,$ U $($$$40,000)$ is $0\mathrm{.}9,$ U $($$$10,000)$ is $0\mathrm{.}6,$ U $($$$5,000)$ is $0\mathrm{.}5,$ U $($$$-10,000)$ is $0\mathrm{.}4,$ and U $($$$-40,000)$ is $0\mathrm{.}0.$ The physicians also have a reliable forecast indicating a $40\%$ probability of the high medical demand. Using expected utility, what alternative should they choose and what is the expected utility of that decision?a$.$medium, $0\mathrm{.}60$b$.$large, $0\mathrm{.}40$c$.$small, $0\mathrm{.}42$d$.$small, $0,44$