How to Calculate Maximum Profit

Suppose:
P = 120 - 0,02 Q
C = 60 Q + 25000

where P is per unit price, Q is quantity, and C is total costs.
TR = Total Revenue
MR = Marginal Revenue
MC - Marginal Cost
How do we get the maximum profit?

Answer:

TR = P x Q
      = (120 - 0,02 Q)Q
TR = 120Q - 0,02Q2
MR = TR'

MR = 120 - 0,04Q

MC = C'
MC = 60

Maximum Profit can be reached when MR = MC.
120 - 0,04Q = 60
0,04Q = 120 - 60
Q = 60/0,04
Q = 1500

Substitute Q to equation P = 120 - 0,02Q, thus:
P = 120 - 0,02(1500)
   = 120 - 30
P = 90

To get maximum profit, the quantity must be 1500 and price must be 90.
Profit max = TR - TC
             = 120Q - 0,02Q2 - (60Q + 25000)
             = 120(1500) - 0,02(1500)2 - 60(1500) - 25000
             = 180000 - 45000 - 90000 - 25000
             = 20000
Thus, the maximum profit is 20.000 !