Frankfurt Electronics produces a component internally using a state$-$of$-$the$-$art technology. The operations manager wants to determine the optimal lot size to ensure that the total annual inventory cost is minimized. The daily production rate for the component is $500$ units, annual demand is $36,000$ units, setup cost is $$150$ per setup, and the annual holding rate is $30$ percent. The manager estimates that the total cost of a finished component is $$80.$ If we assume that the plant operates year$-$round, and there are $360$ days per year, what are the $($a$)$ daily demand, $($b$)$ optimal lot size, $($c$)$ highest inventory, $($d$)$ annual product cost, $($e$)$ annual holding cost, $($f$)$ annual setup cost, $($g$)$ total annual inventory cost, $($h$)$ length of a production period, $($i$)$ length of each inventory cycle, $($j$)$ rate of inventory buildup during the production cycle, and $($k$)$ the number of inventory cycles per year? Plot the movement of the inventory during one production cycle using time on the horizontal axis and on$-$hand inventory on the vertical axis $($see Figure $7\mathrm{.}10).$