Assembly-Line Balancing. A product is assembled from three different parts. The parts are manufactured by two departments at different production rates as given in the following table:

Determine the maximum number of final assembly units that can be produced weekly.

Assembly units = min{units of part 1, units of part 2, and units of part 3}. Maximize z = min{ x₁ , x₂ } is equivalent to max z subject to z ≤ x₁ and z ≤ x₂.

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Department 1 2 Capacity (hr/wk) 100 80 Production rate (units/hr) Part 2 5 12 Part 1 8 6 Part 3 10 4