Lane Accessories has a growing demand for custom Apple watch designer bands. The current manufacturing costs are $120 per hour to operate, for each hour of operation, 210 black band designs and 180 multi-color designs are completed. However, Lane found a new larger manufacturing space that will cost $160 per hour and produce 325 black design bands and 289 multi-color bands per hour completed. Lane has newly placed orders to restock other retail outlets nationwide for 6,000 black band designs and 5,000 multi-color bands. Because Lane is out of inventory, she needs to decide how many hours to operate each facility to fulfill orders while minimizing cost. Formulate the orders for black design bands. A) 210x₁ + 325x₂ $\ge$ 6,000x₃ B) 210x₁ + 325x₂ $\ge$6,000 C) 180x₁ + 210x₂ $\ge$ 6,000 D) 180x₁ + 325x₂ $\ge$ 5,000

Question

Quizplus · Accepted Answer

The correct formulation for the orders of black design bands is based on the production rates of the two facilities for black bands specifically. The first facility produces 210 black bands per hour, and the new facility produces 325 black bands per hour. The goal is to fulfill an order of 6,000 black bands, which matches option B.

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