A firm in a competitive industry produces its output in two plants. Its total cost of producing Q1 units from the first plant is TC1 = (Q1)2, and the marginal cost at this plant is MC1 = 2Q1. The firm's total cost of producing Q2 units from the second plant is TC2 = 2(Q2)2; the marginal cost at this plant is MC2 = 4Q2. The price in the market is P. What fraction of the firm's total supply will be produced at plant 2?