Problem $3.$ A purchasing manager is determining the quantity of items to purchase of a product 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 goes into expedited production by the supplier and the item costs increase by $$100($just for the extra units acquired in a rush and placed in backorder with the customer$).$ The maximum that can be produced in an expedited manner is $75$K units. Overstock above the demand is sold on secondary channels for about $$150($$$30$ loss$).$ Prepare a payoff matrix and provide the conservative and min$-$max regret decisions.