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Accessories has a growing demand for custom Apple watch designer bands. The current nufacturing costs are $$120$ per hour to operate, for each hour of operation, $210$ black band igns and $180$ multi$-$color designs are completed. However, Lane found a new larger hufacturing space that will cost $$160$ per hour and produce $325$ black design bands and $289$ ti$-$color bands per hour. Lane has newly placed orders to restock other retail outlets onwide for $6,000$ black band designs and $5,000$ multi$-$color bands. Because Lane is out of entory, she needs to decide how many hours to operate each facility to fulfill orders while imizing cost. Formulate the orders for black design bands. $($Let $x1=$ number of hours to rate at current facility, $x2=$ number of hours to operate at new facility$)$

a$.180x_1+210x_{2}6,000$

b$.210x_1+325x_{2}6,000x_3$

c$.210x_1+325x_{2}6,000$

d$.180x_1+325x_{2}5,000$