Section 3: Applications of derivatives and differentials to ECON 5. (20pts) (Business: Maximizing Revenue) A stereo manufacturer determines that in order to sell x units of a new stereo, the price per unit, in dollars, must be p(x) = 10 x. The manufacturer also determines that the total cost of producing x units is given by C(x) = 30 + 2x 3) Find the total revenue function R(x}. b) Find the total prot function 750:) with its domain. 0) How many units must the company produce and sell in order to maximize prot? (Hint: you are required to write out FOC, namely, Tc'(x) = 0; solve the equation Tc'(x) = 0 for the critic-a1 value; then apply the Maximum-Minimum Principle 1) d) What is the maximum prot? e) What price per unit must be charged in order to make this maximum prot