(question in description!!!)

Question

A railway company offers excursions at $120 per person for tour groups of up to 100 people. If the size of a group is greater than 100, the company will reduce the price of every ticket by 50 cents for each person in excess of 100. What size tour group would produce the greatest revenue and what ticket price should be charged to produce this revenue? Show your work.

Answer 1

Revenue = (price per unit) . (number of units)

Revenue = (120 - 0.5x) . (100 + x)

= 12000 + 120x - 50x - 0.5x²

= -0.5x² +70x +12000

R(x) = -0.5x² +70x +12000

R^'(x) = -x +70 = 0; x= 70

Price per unit is 120 - 0.5*70 = $85

Tour group size is 100 +70 =170

I hope that helps