Question

The demand function for sunshades is given as:

?=270−2?P=270−2Q

where P is the price paid for a sunshade and Q is the number of sunshades demanded.

The fixed cost is 460 while the cost per shade is 70.

When profit is maximised, the number of sunshades sold =Answer

The maximum profit = Answer

When profit is maximised the marginal revenue, MR = Answer

When profit is maximised the marginal cost, MC = Answer

Answer 1

When profit is maximised, the number of sunshades sold = 50
The maximum profit = 4540
When profit is maximised the marginal revenue, MR = 70
When profit is maximised the marginal cost, MC = 70

Calculation:
Demand = 270 - 2Q; So, MR = 270 - 4Q (MR has double slope); MC = 70
Quantity is where MR = MC; 270 - 4Q = 70, so, Q = 50

Plug in Q = 50 in demand function for price:
270 - 2*50 = 170; So, P = 170

MR = 270 - 4*50 = 70; MR = 70

Profit = [(Price MC) * Quantity] - FC = [(170 - 70)* 50] - 460 = 5000 - 460 = 4540
Also, Profit = Total revenue - Total cost, or
Profit = (Price* quantity) - [FC + (MC*Q)] = (170 * 50) - [(460+(70*50)] = 8500 - 3960 = 4540