A small theatre has a seating capacity of 7700 When the tick

A small theatre has a seating capacity of 7700. When the tickets are priced at $35 attendance is 4500. For each $3 decrease in price, attendance increases by 220.

(1) Make a table for attendance when price equals $32, $29, $26, $38, $41, $44.

(2) Create a graph where the x - axis represents price and the y - axis represents attendance. Then draw all the points from part (1) on this graph. For instance, if price is $35 and attendance is 4500, draw the point (35,4500). Similarly, for the other points. Your graph should contain 7 points.

(3) Using the graph from part (2), decide whether attendance is a a linear, quadratic, polynomial, rational, logarithmic or exponential function of price. Express attendance A as a function of price p .

(4) If attendance is 4500 and price is $35, what is the revenue of the theatre? More generally, if attendance is A and price is p dollars, what is the revenue? (Your answer must contain the variables A,p ).

(5) Use your answers in parts (3) and (4) to express revenue R as a function of price p .

(6) Repeat your work in part II to determine what the maximum revenue of the theatre will be and what price will result in maximum revenue.

Solution