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, five days per week, and demand for each item is normally distributed. The company uses a continuous inventory system. The manager has gathered the following informationabout the itemsGadgetWidgetAverage demand$6,000$ units per year$50$ units per weekStandard deviation$50$ units per week$5$ units per day.Unit cost $($C$)$$$18$$$200$Production rate$100$ units per dayOrdering cost$/$Setup cost$$550$$$2,650$Annual holding cost$10\%15\%$Lead time$3$ weeks$1$ weekService level$99\mathrm{.}5\%97\%$Compute the optimal order quantity for item Gadget.b$.$ How many orders of item Gadget will be placed per year?What should the safety stock be for item Gadget?d$.$Compute the optimal order quantity for Widget.When should the manager reorder item Widget?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?