A manufacturing facility is planning to increase the storage space by building a new high$-$bay warehousing system. An analysis is performed for one of the main products of the facility and the following data are obtained:The annual demand for this product is $10,000$ units.The cost of providing space is $$1$ per unit per day.The combined cost of storing or retrieving a unit is $$0\mathrm{.}50.$The inventory carrying cost rate is $20\%$ based on the average inventory level.The cost of shortage is $$30$ per unit per day.The cost of the product is $$40$ per unit.The cost of production setup is $$200$ per order.The production rate is $50,000$ units per year.The space required for each unit is $2$ ft$\text{'}.$How much space should be allocated for this product such that the total inventory cost is minimized?