Answer to Question #332644 in Calculus for Olga

Question

A firm has the following total and cost functions:

TR=20Q−4Q^2

TC=16−Q^2,

where Q is the number of unites produced and sold (in thousands). How many units should be produced to maximise the profit?

a.3,3333,333 units.

b.1,7141,714 units.

c.1,3331,333 units.

d.3 3333 333 units.

Answer 1

Profit = TR - TC = 20Q - 4Q²Â - (16 - Q²) = 20Q - 4Q²Â - 16+ Q²Â = 20Q-16- 3Q²

Profit has maximum, then

$\frac{d Profit}{d Q} = 20 - 3*2*Q = 0\\ Q=20/6=3.3333\\ Answer:a$