Tiernan, Inc., purchases an electronic component EC$-1002$ from its supplier. The purchase cost of the component is $$20.$ The company$$s supply manager estimated the demand of $30,000$ components for the next year. Holding costs for the components are $20\%$ and it costs $$1,500$ to place an order with the printer. The supplier provides the following discount schedule:

Order Size Range Discount

$($Units$)(\%)$

$04,4990\%$

$4,5009,9991\mathrm{.}25\%$

$10,000$ and More $2\mathrm{.}5\%$

a$)$ Determine the order quantity that minimizes the total material cost $($i$.$e$.$ total purchase cost and total inventory cost

b$)$ If company operates $300$ days per year, determine the cycle time $($i$.$e$.,$ time between two orders$).$