The production function relates outputs (y1, y2, y3, y4, y5) to inputs (y1, y2, y3, y4) with given prices. External constraints fix production levels of y1=7, y2=6, and y3=27. The firm faces a problem where the constrained production levels may not maximize profits given input and output prices. A graph can illustrate the constrained production possibility set and equilibrium conditions, showing the optimal production levels are not achievable given the constraints.