A drug company has a monopoly on a new patented medicine. The product can be made in either of two plants. The marginal costs of production for the two plants are

MC1=30+2Q1

and

MC2=10+4Q2.

The? firm's estimate of demand for the product is

P=30−3Q1+Q2.

How much should the firm plan to produce in each? plant? At what price should it plan to sell the? product? ?(Round your responses to two decimal? places.)

The firm should produce 0 units in plant 1 and 2 units in plant 2. 

To maximize profits, it should charge a price of $24 per unit.

Step-by-step explanation

The marginal cost of first plant is irrelevant since it lies above the demand curve. 

The maximum price is $ 30 and the marginal cost of plant 1 is $ 30 and it lies above the demand curve.

Therefore, the firm will not produce any output in plant 1.

Therefore, the marginal cost curve of plant 2 will be considered and the demand curve is;

P = 30 - 3Q2

TR2 = P × Q2 = 30Q2 - 3Q2²

MR2 = 30 - 6Q2

Equate it to MC

30 - 6Q2 = 10 + 4Q2

10Q2 = 20

Q2 = 2.0

Price, P = 30 - 3(0 + 2) = $ 24