A cruise line estimates that it can sell 3,400 tours to Alaska at a price of $900 each, but it will lose 100 sales for each $50 increase in its price. Let p be the price and q the number of tours sold.

(a) Write q as a linear function of p.

(b) Write the revenue R as a function of p and find the marginal revenue with respect to p (i.e., the rate of change of R with respect to p).

(c) Suppose it costs $400 per passenger to operate the tour. Write the cost as a function of the price p and find the marginal cost with respect to p.

(d) Find the marginal profit with respect to p.

(e) The company priced its tour at $1,050 last year. If it increases the price this year, will it increase or decrease its profit? Explain your answer.

(f) Answer the same question and explain your answer if last years price was $1,550.