Suppose M $=500$ units, C $=$ $$10$ per unit, and a full carload of $500$ units costs $$3,000.$ a$)$ Develop and interpret a graph of average cost per unit, C$($Q$)/$Q$,$ assuming the schedule. b$)$ Suppose that the units are consumed at a rate of $800$ per week, order setup cost is $$2,500,$ and holding costs are based on an annual interest charge of $22\%.$ Graph the function G$($Q$)=()=\backslash$lambda C$($Q$)/$Q $+$ k$\backslash$lambda $/$Q $+$ I$($C$($Q$)/$Q$)$Q$/2$ and find the optimal value of Q$.($Assume that $1$ year $=50$ weeks$)$ c$)$ Repeat part $($b$)$ for $\backslash$lambda $=1,000$ per week and K $=$ $$1,500$ and comment on the difference observed.