The demand for a new locally produced soap is given by p(q) = 53/sqrt(q) where 'q' is the number of bars of soap and 'p(q)' is price in dollars. The cost of manufacturing the bars of soap is linear with a fixed cost of $608 and marginal costs of $0.53 per bar. Find the number of bars of soap that should be manufactured to produce the maximum profit and the maximum profit, if the company has a present production capacity of 7530 bars of soap

1. What is the domain of this problem? Why do you know this?

2. What is the equation for the cost function, C(q)?

3. What is the equation for the revenue function, R(q)?

4. What is the equation for the profit function, P_r(q)?

5. What are you trying to maximize?