Question

1. A firm produces at a profiting maximizing quantity. The price of their product is $56 and the total cost function is TC=2Q³+2Q-64. What is the profit maximizing quantity?
   1. 6
   2. 2
   3. 3
   4. Need more information

Answer 1

The price is given as $56.

The total revenue is the product of price and quantity. So, tbe total revenue is 56Q when Q units are produced.

The tot cost function is given as:

TC = 2Q³ + 2Q - 64

The profit can be calculated by the following formula:

Profit (π) = Total Revenue - Total Cost

Profit = 56Q - 2Q³ - 2Q + 64 = -2Q³ + 54Q - 64

Differentiating with respect to Q:

dπ/dQ = -6Q² + 54

Putting it equal to 0:

6Q² = 54

Q = 3

Checking that the profit is maximum or minimum:

d²π/dQ² = -12Q < 0

So, the profit is maximizes when 3 units are produced. Therefore, the correct answer is 'Option C'.