Please you need the answer with some explanation.
A local daily newspaper with a circulation of 80,000 subscribers is thinking of raising its subscription price. Currently the price is $1.50 per week, and it is estimated that the paper would lose 5,000 subscribers if the rate were to be raised by ten cents/week.
(a) Find the subscription price that maximizes profit. Use the five-step method, and model as a one-variable optimization problem.
(b) Examine the sensitivity of your answer in part (a) to the assumption of 5,000 lost subscribers. Calculate the optimal subscription rate assuming that this parameter is 3,000, 4,000, 5,000, 6,000, or 7,000.
(c) Let n = 5, 000 denote the number of subscribers lost when the sub- scription price increases by ten cents. Calculate the optimal subscrip- tion price p as a function of n, and use this formula to determine the sensitivity S(p, n).
(d) Should the paper change its subscription price? Justify your conclu- sions in plain English.