A factory is able to manufacture smart watches at an expense of $50 per unit. The projected market behavior suggests that if the watches are priced at p dollars each, customers will purchase = 120 watches monthly.

a. Formulate the factory's profit P as a function of q? b. What's the average rate of profit fluctuation as the production escalates from q = 0 to q = 20?

c. What's the rate of change in profit when q = 20 watches are manufactured? Is the profit on an upward or downward trend at this level of production?