Aggregation with a capacity constraint

WW Grainger sources products from many suppliers and is considering aggregation of its inbound shipments to lower costs. In particular, WWG is considering $3$ suppliers. WWG procures $12000$ units of product annually from each of these three vendors. WWG uses a third$-$party logistics $(3$PL$)$ contractor, who charges a fixed transportation cost of $$3000$ per order delivery $($regardless of order size$).$ The $3$PL company also charges $$200$ per pickup. Each unit of the three products costs $$150$ and WWG incurs a holding cost of $20\%.$ Grainger is considering whether aggregating products $($joint ordering and delivery$)$ from all $3$ suppliers in one periodic inbound shipment.

a$)$ What is the optimal order frequency and order size if not aggregate? What is the total cost?

b$)$ What is the optimal order frequency and order size if aggregate? What is the total cost?

c$)$ If the truck has a capacity of $2000$ units, is the plan from part $($b$)$ feasible. If not, suggest an alternative plan.