Consider the three$-$period inventory problem. The firm has to decide how many units should be produced to meet each period's demand. The setup cost is $ $5$ and the variable cost is $ $2.$ The holding cost is $ $1$ per unit per month. Inventory at the end of each period cannot exceed $2$ units. Initial inventory is $0.$ Demand for each period is equally likely to be $0$ or $1$ unit.Each unit demanded can be sold for $$4.$ If the demand is not met on time, the sale is lost. Use dynamic programming to maximize the expected profit earned during three periods.What is the optimal action if we enter period $2$ with a beginning inventory of $1$ units?