PROBLEM #$1$: A production manager needs to develop a production schedule to meet the following demand: Period $34$ Demand $50013001600500$ production costs are as follows: production cost during regular time: $$4$ per unit cost of subcontracting: $$5$ per unit Inventory carrying cost $=$ $$3$ per unit per period Back$-$order costs $=$ $$8$ per unit per period. Regular production rate: $900$ units per period You can subcontract at the rate of $150$ units per period only during the second and third periods. Develop a production schedule for this scenario and answer the following questions. Equation: Surplus$/$Shortage in any period $=$ Quantity Produced $+$ Quantity Subcontracted $-$ DemandWhat is the surplus or shortage in the second period?