Answer to Question #333794 in Algebra for Tebu

Question

TR = 20Q - 4Q

TC = 16 - Q

How many units should be produced to maximise the profit?

Answer 1

$$Profit=P=TR-TC$$

$$=20Q - 4Q^2-(16 - Q^2)$$

$$=-3Q^2+20Q-16$$

Differentiate with respect to $Q$

$$dP/dQ=-6Q+20$$

$$dP/dQ=0=>-6Q+20=0$$

$$Q=10/3$$

3.3333333 units.