Question $1(2+2+2+2+2=10$ points$)-$Discrete demand for newsvendor model Holiday Gift shop places orders for Christmas items during a trade show in July. One item to be ordered is a dated sterling silver tree ornament. Each ornament costs $$60$ when ordered in July. The ornaments will sell for $$100.$ Ornaments unsold by Christmas will be on clearance with a $60\%$ off and always sell during January $.100$ The best estimate for demand is: Demand $708090$ Probability $($PDF$)0\mathrm{.}20\mathrm{.}3$ CDF $0\mathrm{.}250\mathrm{.}50\mathrm{.}75$ a$)$ What is the mean demand $?($Hint : sum up all x$*$ Pr$($D$=$x$).)0\mathrm{.}30\mathrm{.}21\mathrm{.}0$ E$($X$)=70^*0\mathrm{.}2+80^*0\mathrm{.}3+90^*0\mathrm{.}3+100^*0\mathrm{.}2=85$ b$)$ What is the newsvendor critical ratio $?$ C$\_\{$s$\}/($C$\_\{4\}+$ C$\_\{$e$\})=(100-60)/(40+(60-24))=40/76=0\mathrm{.}5263$ c$)$ What is the optimal number of ornament Q$^*$ to order $?$