Demand for a product is determined by the function p = 32 - 0,01q. What is the price and the quantity of the product under the maximum revenue?

Question 3:

(a)    Demand for a product is determined by the function p = 32 - 0,01q. What is the price and the quantity of the product under the maximum revenue?
(b)     Revenue is determined by the function R(q) = 46q - q2, cost is determined by the function C(q) = 5q2+ 10q + 3. Find the maximum revenue and profit.  
(c)     A company sells jeans for $85 each. If the cost of the production is determined by the formula C(q) = q2 + 25q+50, then, how many jeans we need to produce and sell in order to maximize profit?
(d)     The cost of the production is determined by the formula C(q) = 2q2 + 12q + 30. How many products we need to produce in order to maximize profit, provided that the price of the product is $60? 
(e)    T-shirts are sold for 46 soms each. Provided that the cost of the production is determined by the function C (q) = 120 + 30q + 0,1q2, find the highest possible profit.