$1.$ ?Toy $-$ N $-$ Toy Company has a steady and constant demand of $12,000$ ?Type $-$ X toys per year. TNT $\text{'}$ s production department estimated $ $240$ ?per production setup to make Type $-$ X toys $($ Co $).$ ?It costs $ $12\mathrm{.}00$ ?per Type $-$ X toy to hold $($ carry $)$ ?for a year. The production department calculated the daily production rate of $180$ ?Type $-$ X toys with increment of $10$ ?Type $-$ X toys. The TNT Company operates $250$ ?days per year. The production cost $($ r $)$ ?is calculated as $ $7\mathrm{.}50$ ?per Type $-$ X toy. Determine: a $)$ ?Optimal batch size of Type $-$ X toys to produce. $(12)(4)$ ?b $)$ ?Maximum inventory level of Type $-$ X toys. c $)$ ?TNT $\text{'}$ s ICM $($ Inventory Control and Management $)$ ?section allocated space for Type $-$ X toy to hold a maximum of $510$ ?type $-$ x toys. Determine and specify the effect of allocated space on the batch size and corresponding total inventory cost. $(8)$ ?d $)$ ?Due to the sudden increase on demand on other products, the production department re $-$ assigned production resources to accommodate the sudden increase in demand. As a result, the daily production rate of Type $-$ X toys decreased to $100$ ?per day. i $.$ ?What should be the new batch size? $(8)(4)$ ?ii $.$ ?What is the new yearly Total Cost for Type $-$ X toys? iii. Does this reduction in production rate of Type $-$ X toy satisfy the storage space limitation $?$ ?Justify your answer. $(4)$