Tastes for your consumers can be modelled by the utility function

U(x₁, x₂)=10x₁^0.5+ x₂, where x₁=x represents amusement park rides and x₂ represents dollars of

other consumption. Suppose further that your marginal cost function is given by MC(x)= x/250,000.

a. Suppose that you have 10,000 consumers on any given day. Calculate the (aggregate) demand

function for amusement park rides.

b. What price would you charge if your goal was to maximize total surplus? How many rides

would be consumed?

c. In the absence of fixed costs, what would your profit be at that price?