1. The expression for the total profit is given by:

profit = x × Q(x) − C(x) = x × (100 − 0.01x) − (50x + 10,000) = −0.01x2 + 50x − 10,000 To maximise the profit we are required to differentiate the function and set the derivative equal to zero, i.e.

−0.02x + 50 = 0 and we find:

x =

50 0.02

= 2,500 The profit associated with this value is given by:

profit = −0.01 × 2,5002 + 50 × 2,500 − 10,000 = £52,500 x = 2,500 and the total profit £52,500.