How many units must be produced and sold to make the profit a maximum?

Question

the marginal profit (in dollar per unit) when x units are produced and sold is given by p'(x)= -0.6x^2+70. The number of units that must be produced and sold to make the profit a maximum is:

Answer 1

P'(x) = - 0.6x² + 70 = 0; x² = 70/06; x = √(70/06) = 11 units.

Now, P''(x) = - 1.2x; P''(11) = -1.2·11 = - 13.2 < 0. So, at x = 11 we have maximum profit