Finding the Optimum Point Graphically for a Two-Phase Problem

Recall the Acme Bicycle Company Example that was discussed in the notes and previous examples: 


x₁: mountain bikes to produce (bikes/day)

x₂: racers to produce  (bikes/day)

Variable non-negativity:

x₁ ≥ 0,  x₂ ≥ 0

Objective Function:

Maximize daily profit ($/day):  Max z =  15 x₁ + 10 x₂


Mountain bike production limit (bikes/day): x₁ ≤ 2

Racer production limit (bikes/day): x₂ ≤ 3

Metal finishing machine production limit (bikes/day): x₁ + x₂ ≤ 4