Consider a monopolist that has two plants. Plant 1 has a cost function of C (91) = 2q and Plant 2 has a cost function given by C2 (92) = 92. Observe that both plants have increasing marginal cost. (i) Argue that, for any given quantity q = 9 +92 that the firm has to produce, it will split production across the two plants such that the marginal cost of production is the same at the two plants. (ii) Find the cost function for the firm to produce a quantity q after it optimally splits production across its two plants.