PA $12-5($Static$)$ BZoom sells toy bricks that can used to construct...

BZoom sells toy bricks that can be used to construct a wide range of machines, animals, buildings, and so on$.$ It purchases a red dye

powder to include in the resin it uses to make the bricks. The powder is purchased from a supplier for $$1\mathrm{.}3$ per kilogram. At one

Costs

production facility, BZoom requires $400$ kilograms of this red dye po

and the fixed cost associated with each order to the supplier is $$50.$

a$.$ How many kilograms should BZoom order from its supplier with each order to minimize the sum of the ordering and holding costs?

b$.$ If BZoom orders $4,000$ kilograms at a time, what would be the sum of the annual ordering and holding costs?

Costs

c$.$ If BZoom orders $2,000$ kilograms at a time, what would be the sum of the ordering and holding costs per kilogram of dye?

Note: Round your answer to $3$ decimal places.

Costs

per kilogram