CDF Appliances has assembly plants in Atlanta and Fort Worth where it produces a

Question

CDF Appliances has assembly plants in Atlanta and Fort Worth where it produces a variety of kitchen appliances, including a 12-cup coffee maker and a cappuccino machine. In each hour at the Atlanta plant, 160 of the coffee makers and 200 of the cappuccino machines can be assembled, and the hourly cost is $900. In each hour at the Fort Worth plant, 800 of the coffee makers and 200 of the cappuccino machines can be assembled, and the hourly cost is $2700. CDF Appliances expects orders each week for at least 56,000 of the coffee makers and at least 30,000 of the cappuccino machines. How many hours per week should each plant be operated in order to provide inventory for the orders at minimum cost?

Find the minimum cost per week

Explanation / Answer

Let the number of hours that Atlanta plant is functional is A

Let the number of hours that Fort Worth plant is functional is F

Minimize cost, i.e. 900A + 2700F

constraint: 160A + 800F >= 56000 [coffee maker]

200A + 200F >= 30,000 [cappuccino machine]

Solving the LP, we get

A = 100, F = 50

and the minimum cost is $ 225,000

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