$6$: Linear Programming

$30.$ Minimizing Shipping Costs Steinwelt Piano manufactures upright and console pianos in two plants, Plant I and Plant II$.$ The output of Plant I is at most $\frac{300}{?}$ month, whereas the output of Plant II is at most $\frac{250}{?}$ month. These pianos are shipped to three warehouses, which serve as distribution centers for the company. To fill current and projected future orders, Warehouse A requires at least $200$ pianos$/$month$,$ Warehouse $B$ requires at least $150$ pianos$/$month$,$ and Warehouse $C$ requires at least $200$ pianos$/$month$.$ The shipping cost of each piazo from Plant I to Warehouse $A,$ Warehouse $B,$ and Warehouse $C$ is $$60,$$$60,$ and $$80,$ respectively, and the shipping cost of each piano from Plant II to Warehouse $A,$ Warehouse $B,$ and Warehouse $C$ is $$80,$$$70,$ and $$50,$ respectively. What shipping schedule will enable Steinwelt to meet the warehouses' requirements while keeping shipping costs to a minimum?