A firm is attempting to minimize its shipping costs. The firm has $3$ factories and must supply the needs of its $3$ customers without shortages. Since the firm has no storage facilities, each factory must make daily shipments to its customers. The table below shows the capacity of each factory, the amount required by each customer, and the cost of shipping from each factory to each customer.

Shipping Costs $($$$/$unit$)$

Factory$/$Capacity Customer $1$ Customer $2$ Customer $3$

A$/160$ units $131013$

B$/180$ units $11149$

C$/200$ units $141012$

Requirement$270$ units Requirement$90$ units Requirement$180$ units