FCC Cafeteria, which is a fast lunch spot in $$ankaya University campus,

purchases several basic cooking ingredients from a supplier. The annual usage $($demand$),$ purchasing cost,

and setup $($order$)$ cost of these ingredients are given in the table below. The inventory carrying rate is $0\mathrm{.}10$

per unit per year.

Ingredient A B C

Annual Demand $($in units$)1,0002,0001,000$

Setup Cost $($$ $/$ order$)243$

Purchasing Cost $($$ $/$ unit$)416$

$($a$)$ Assume that all ingredients are ordered independently. What is the total inventory carrying cost of all

ingredients when all ingredients are optimally ordered?

$($b$)$ The cafeteria management wants to order all ingredients in each cycle,