Nate plans a charity concert in the school hall.
The school provides him with the following information to determine the maximum number of concert tickets that can be sold.
Safety directives
To ensure safe emergency evacuation, there must be a semicircular clear zone with a radius of 1 m in front of each exit.
The usable area excludes the stage, the sound booth and the clear zones.
Standing Zone: maximum crowd density is 1.4 persons per m\(^2\) of usable area.
Seated Zone: maximum crowd density is 1.0 persons per m\(^2\) of usable area.
Floor plan of the hall drawn accurately to a scale of 1 : 400
Find the maximum number of standing concert tickets that can be sold.
Give your answer correct to the nearest whole number.[4]
Nate considers two ticketing options and their associated logistical costs.
Ticketing Option 1: Pure Standing Setup
Ticketing Option 2: Hybrid Setup (Seated + Standing)
The usable area is divided into three distinct zones: the Seated Zone that is nearest the stage, followed by the Safety Zone, then the Standing Zone.
The Safety Zone is a horizontal strip, 1.2 m wide, separating the Seated Zone from the Standing Zone.
After excluding the Safety Zone, the remaining usable area is divided in the ratio 3 : 2 between the Seated Zone and the Standing Zone respectively.
Seated tickets: \$32 per ticket
Standing ticket: \$15 per ticket
Logistical Costs
Fixed setup cost: The logistics team charges a fixed fee of \$1500 for Option 1. This fee is 20% higher for Option 2 due to the additional logistics required for chair installation.
Transaction fee: A fee of \$1.50 is charged by the online ticketing vendor for every ticket sold.
Determine the option that Nate should select.
Justify the decision you make and show your calculations clearly.[7]