QUESTIONS:$1.$A retail chain has $6$stores in a region supplied from $3$ supply sources. Trucks have a capacity of $25,000$ units and cost $$(1000+3*$X$)$per load plus $$(100-$X$/2)$per delivery. The cost of holding one unit in inventory at retail for a year is $$1\mathrm{.}5.$ The managers will set upmilk runs from suppliers to retail stores. Assume that all trucks travel full. Suppliers are considering whether to run a milk run to $2$ stores or $3$stores on each truck. Determine a demand threshold in selection of the two options given$\mathrm{.}2.$Weekly demand for motors is normally distributed with a mean of $1,500$ and a standard deviation of $(1,000+$X$).$ Motors are currently assembled in Taiwan and delivered at a cost of $(1,900+3*$X$)$$$/$motor$.$ The supplier takes fourweeks to supply an order. A domestic manufacturer has offered to supply motors with a lead time of $1\mathrm{.}5$ weeks on averageat a cost of $(2,150+$X$)$$$/$motor$.$ The motor manufacturer is targeting a CSL of $99\mathrm{.}5$percent and monitors its inventory continuously. The manufacturer incurs a holding cost of $30\%.$ Should the manufacturer accept the local supplier$$s offer?$3.$Demand for specific a spare part is $(20,000+10*$X$)$boxes per month. The holding cost is $25\%$ per year. Eachorder incurs a fixed cost of $$1,000.$ The supplier wants to offer aquantity discount pricing scheme with a price of $$5$ per box for the first $30,000,$a price of $$4\mathrm{.}90$ per unit for the quantity between $30,000$ and $50,000,$ and $$4\mathrm{.}70$ per unit for the quantity above $50,000$ units. a$.$Analyze all unit quantity discount systemfor this case.b$.$Analyzethe marginal unit quantity discount systemfor this case.c$.$Compare two systems and interpret$\mathrm{.}4.$STGcompany has introduced a new device which is sold through aretailerstore. The store managerhas estimated that demand will depend on the final retail price paccording to the demand curve: $=1,500,000+201,500.$ The production cost for STGis $$200$per product.What wholesale price should STGcharge?