Please give me a very detailed answer and use the Lagrange function to solve it. If you need to draw a picture to explain it, please draw the picture too

6. A drug company has a monopoly on a new patented medicine. The product can be made in either of two plants. The total costs of production for the two plants (Plant 1 and Plant 2) are given by: TC,(Q,) = 10Q; TC,(Q,) = 20Q3 where @ and are the level of output produced by Plant 1 and Plant 2, respectively. The firm's estimate of demand for the product is given by P=20-3(Q, +0,) where P is the unit price of the product. (a) Suppose that this company 1s not able to price discriminate. What are the profit maximizing level of output produced by Plant 1 and Plant 2? (b) At what price will it sell the product