Her operations manager is considering a new$$ plan, which begins in January with units on hand and ends with zero inventory. Stockout cost of lost sales is $$$ per unit. Inventory holding cost is $$$ per unit per month. Ignore any$$ idle$-$time costs. The plan is called plan B$.$

Plan$$ B: Produce at a constant rate of units per$$ month, which will meet minimum demands. Then use$$ subcontracting, with additional units at a premium price of $$$ per unit. Subcontracting capacity is limited to units per month. Evaluate this plan by computing the costs for January through August.