Problem $3.$ A purchasing manager is determining the quantity of items to purchase of aproduct family for the upcoming summer season. There are $4$ demand scenarios: $100$k$,150$k$,200$k$,$ or $250$k units. The options are to purchase at the same $4$ levels of demand.Each item costs $$180$ and sells for $$300.$ Demand unsatisfied by the initial stock goesinto expedited production by the supplier and the item costs increase by $$100($just forthe extra units acquired in a rush and placed in backorder with the customer$).$ Themaximum that can be produced in an expedited manner is $75$K units. Overstock abovethe demand is sold on secondary channels for about $$150($$$30$ loss$).$ Prepare a payoffmatrix and provide the conservative and min$-$max regredecision.