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 $600. 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 $2400. CDF Appliances expects orders each week for at least 80,000 of the coffee makers and at least 28,000 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

Cappuccino machines should be produced in Atlanta and coffee makers in Fort Worth. The Fort Worth facility would need to operate 100 hours per week and the Atlanta facility would need to operate 140 hours per week.

Total costs associated to operating the facilities = ($2,400 x 100) + ($600 x 140) = $324,000

Explanation:

Since there is not constraint regarding the total number of labor hours that each plant can operate, then we must choose the plant that operates at the lower cost. The only restriction is total time = 7 days x 24 hours = 168 hours per week:

production costs Atlanta:

coffee maker = $600 / 160 = $3.75 per unit

cappuccino machine = $600 / 200 = $3 per unit

production costs Fort Worth:

coffee maker = $2,400 / 800 = $3 per unit

cappuccino machine = $2,400 / 200 = $6 per unit

Cappuccino machines should be produced in Atlanta and coffee makers in Fort Worth. The Fort Worth facility would need to operate 100 hours per week and the Atlanta facility would need to operate 140 hours per week.

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