Here is my questiionAn auto manufacturer uses $500$ tons of steel per day. The company pays $$1,100$ per ton of steel

purchased, and each order incurs a fixed cost of $$2,250.$ The annual holding cost rate, $i$ is $0\mathrm{.}25.$ Now we

will try to see if there are any benefits to allowing shortages for this company. Note that this company

uses steel for a manufacturing process. The shortages will be treated as backorders since the auto

manufacturer will wait for the steel to be delivered. As such, shortages of this supply results in the

production line to halt so there may be big consequence to shortages. $($In the case of this manufacturer,

luckily, the production line is used to manufacture another model so during the backorder period the

line is used for something else.$)$ The management is estimating that the backorder cost, $b$ per unit per

unit time is $$475.$

$($a$)$ Calculate the optimal ordering quantity, Q$*.$

$($b$)$ Calculate the optimal backorder quantity, B$*.$

$($c$)$ What is the overall cost of this optimal policy you have calculated?

$($d$)$ How much lower is the above calculated cost in comparison to the total annual cost you