Children’s Zoo Tour Service By, Thais Santos, Phoebe Cohen, Lucie Thorpe, Chris Lano

Leading Information We operate a Zoo Tour Service We operate a Zoo Tour Service Rates: $ per person (50 people min.) Rates: $ per person (50 people min.) For each additional person (after 50 people) rate is reduced by $2.00 per person. (Max 80 people) For each additional person (after 50 people) rate is reduced by $2.00 per person. (Max 80 people) Cost: $6, (Plus $32.00 per person) for us to pay for the tour bus Cost: $6, (Plus $32.00 per person) for us to pay for the tour bus

THE PROBLEM ! HOW MANY PEOPLE SHOULD BE ON OUR TOUR TO MAXIMIZE OUR PROFIT?

Step One: Figure out the variables of each part of the equation. Figure out the variables of each part of the equation. Make ‘X’ equal the number of additional people. Make ‘X’ equal the number of additional people x = Number of people. 200 – 2x = The amount of revenue we would make. 200 – 2x = The amount of revenue we would make.

Examples: X = 1 [number of people is 51, each person pays $198) X = 1 [number of people is 51, each person pays $198) = = – 2(1) = $ – 2(1) = $198 X = 2 [number of people is 52, each person pays $196] X = 2 [number of people is 52, each person pays $196] = = – 2(2) = $ – 2(2) = $196

Step Two: Calculate the revenue equation Calculate the revenue equation FOIL the two equations FOIL the two equations (50 + x) (200 – 2x) (50 + x) (200 – 2x) 10,000 – 100x + 200x -2x 2 10,000 – 100x + 200x -2x 2 10, x – 2x 2 10, x – 2x 2 -2x x + 10,000 -2x x + 10,000

Step Three: Figure out the equation for the cost to pay for the bus ($ per person) Figure out the equation for the cost to pay for the bus ($ per person) X = number of additional people X = number of additional people Cost Equation = $ (50 + x) = x Cost Equation = $ (50 + x) = x Subtract the cost equation from the revenue equation Subtract the cost equation from the revenue equation (-2x x + 10,000) – ( x) (-2x x + 10,000) – ( x) -2x x +2,400 -2x x +2,400

Step Four: To find the maximum profit (the biggest amount of money you can make), find the vertex of the equation To find the maximum profit (the biggest amount of money you can make), find the vertex of the equation The coefficient in the x 2 is negative, so you know that the graph will be a frowny-face! The coefficient in the x 2 is negative, so you know that the graph will be a frowny-face! Vertex = -b/2a Vertex = -b/2a -68/-4 = /-4 = 17 VERTEX = 17 VERTEX = = = 67

YOU DID IT! 67 PEOPLE WILL MAXIMIZE YOUR PROFIT!!!