$($Risk$-$pooling via centralizing inventory at the $CDC)$ A firm uses a central distribution

center $($CDC$)$ and multiple regional distribution centers $($RDCs$)$ to meet demand across

different regions in the country. The goal is to minimize the total cost, which includes

transportation costs and inventory holding costs, while simultaneously ensuring that

demand of all customers is met.

Input Data:

Demand at each RDC $($monthly$)$:

RDC $1$: $100$ units

RDC $2$: $150$ units

RDC $3$: $200$ units

Transportation Costs from CDC to RDCs $($per unit$)$:

CDC to RDC $1$: $$2$

CDC to RDC $2$: $$3$

CDC to RDC $3$: $$4$

Inventory Holding Costs at each RDC $($monthly per unit$)$:

RDC $1$: $$1$

RDC $2$: $$1\mathrm{.}5$

RDC $3$: $$2$