Problem $5($Adapted from Winston, $2004)$: A company supplies goods to three customers, who each

require $30$ units. The company has two warehouses. Warehouse $1$ has $40$ units available, and warehouse

$2$ has $30$ units

There is a penalty for each unmet unit of customer demand: With customer $1,$ a penalty of $$90$ is

incurred; with customer $2,$$$80$; and with customer $3,$$$110.$

Formulate a balanced transportation problem to minimize the sum of shortage and shipping costs. For

this problem, you should provide a drawing of the minimum$-$cost flow network. Explain in words what

nodes and arcs represent, and label nodes and arcs with all relevant data.