A manufacturer of fine pens produces in two plants. The total cost of producing in the first plant is given by
TC1=y21+100TC1=y12+100.
The total cost of producing in the second plant is given by
TC2=y323+200TC2=y233+200.
In these cost functions, y1y1 corresponds to the number of pens produced in the first plant, and y2y2 corresponds to the number of pens produced in the second plant. Suppose the firm is producing 24 fine pens. If the firm is minimizing costs, it must be producing pens in the first plant. In these cost functions, y1y1 corresponds to the number of pens produced in the first plant, and y2y2 corresponds to the number of pens produced in the second plant. Suppose the firm is producing 24 fine pens. If the firm is minimizing costs, it must be producing pens in the first plant.