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

production facility, BZoom requires $400$ kilograms of this red dye powder each week. BZoom's annual holding costs are $30$ percent

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?

Costs

kilograms

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 kilograme. BZoom's purchasing manager negotiated with its supplier to get a $2\mathrm{.}5$ percent discount on orders of $10,000$ kilograms or greater.

What would be the change in BZoom's annual total cost $($purchasing$,$ ordering, and holding$)$ if it took advantage of this deal instead

of ordering smaller quantities at the full price?

It would decrease by more than $$1,000.$

It would decrease by less than $$1,000.$

It would increase by less than $$1,000.$

It would increase by more than $$1,000.$