$(10$ points$)$ Generic Co$.$ produces hand $-$made children's toys with a capacity of $24$ toys a day, $300$ days a year. Their annual demand is $500$ toys. The unit variable cost of a toy is $$22$ while fixed cost for is $$100$ while the storage and insurance for finished goods costs $$20$ per year per toy $(3$ pts$)$ Compute the optimal production batch size b$(3$ pts$)$ Compute the maximum level of inventory in each cycle $(4$ pts$)$ Generic Co$.$ considers buying from Distinct Inc., a supplier that makes mass produced toys for $$20$ with an ordering cost of $$200.$ Would this decision help decreasing their costs $?$