Student Council organizes an annual out-of-town concert, including transportation. The cost is $140/person and all seats are filled. This year the price will increase. Survey shows that for every $10 increase in price, 5 fewer students will attend. Revenue: R(n) = (140 + 10n)(200 - 5n), where R is Revenue and n is the number of $10 increases in price. a) What Revenue will Students Council make if they raise the cost to $160 ? b) Find R'(n) * HINT: expand first c) When is the slope of the tangent to R(n) equal to zero? ie) Calculate when R'(n) = 0 d) Explain how the derivative of the Revenue function and the maximum Revenue are related. A sketch would be quite useful in this explanation. In the sketch, be sure to use points and label the sketched functions. DRAW/WRITE on the sketch to illustrate/explain the connection. Explanation will need to have numbers and units ($, people/students)