A manager must set up inventory ordering systems for two new items, Gadget and Widget. Gadget is ordered from a supplier and is delivered at once, while Widget is produced in$-$house in batches of fixed size. The company operates $52$ weeks a year and demand for each item is normally distributed. The company uses a continuous inventory system. The manager has gathered the following information about the items. GadgetWidgetAverage demand$7,000$ units per year$50$ units per weekStandard deviation$80$ units per week$15$ units per dayUnit cost $($C$)$$$28$$$350$Production rate $($pt$)-100$ units per dayOrdering cost$/$Setup cost $($Co$)$$$750$$$4,650$Annual carrying cost $($Cc$)18\%25\%$Lead time $($Lt$)3$ weeks$1$ weekService level $()99\mathrm{.}5\%92\%$ a$.$ Compute the optimal order quantity for item Gadget.b$.$ How many orders of item Gadget will be placed per year?c$.$ What should the safety stock be for item Gadget?d$.$ Compute the optimal order quantity for Widget.e$.$ When should the manager reorder item Widget?f$.$ Determine the length of each production run of item Widget, in days.g$.$ What is the time between two consecutive orders of Widget, in weeks?