An event organiser is organising a 3-day Pet Festival for 300 exhibitors. The event organiser charges each exhibitor a registration fee of $90 and a daily booth rental of $150. The event organiser needs to rent an exhibition space for the Pet Festival. The spaces required for the exhibition are as follows: In order to set up the exhibition, the event organiser needs to rent the hall(s) and the items needed one day before the start of the 3-day Pet Festival. Items needed for the exhibition and their rental fees are as follows:

1. Find the total amount collected from one exhibitor

Registration fee $= \char36{}90$

Daily booth rental for 3 days $= 3 \times \char36{}150 = \char36{}450$

Total collected from each exhibitor
$= 90 + 450 = 540$

1. Calculate the total exhibition space required

Area occupied by booths:
$300 \times 15 = 4500\text{ m}^2$
Aisle and open space required:
$65\% \times 4500 = 2925\text{ m}^2$
Total area required:
$4500 + 2925 = 7425\text{ m}^2$

2. Choose the cheapest suitable adjacent hall combination

A single hall is not large enough, so two adjacent halls are needed.

Suitable adjacent combinations include:
$\text{Hall B + Hall C}: 3500 + 4000 = 7500\text{ m}^2,\quad \$6000 + \$8000 = \$14000$
$\text{Hall C + Hall E}: 4000 + 3600 = 7600\text{ m}^2,\quad \$8000 + \$5400 = \$13400$
$\text{Hall D + Hall E}: 3900 + 3600 = 7500\text{ m}^2,\quad \$8200 + \$5400 = \$13600$
The minimum daily rental is therefore
$\$13400.$

1. Calculate the total income collected from exhibitors and visitors

Using part (a), amount collected from each exhibitor is $540.

Income from exhibitors:
$300 \times 540 = \char36{}162\,000$

Income from visitors:
$35\,000 \times 6 = \char36{}210\,000$

Total income:
$162\,000 + 210\,000 = \char36{}372\,000$

2. Calculate the total hall rental cost for the full rental period

Using part (b), daily rental of halls needed is $13 400.

The halls are rented one day before the exhibition and for the 3 exhibition days, so the total rental period is $4$ days.

Hall rental cost:
$13\,400 \times 4 = \char36{}53\,600$

3. Calculate the daily rental cost of all tables and chairs

For $300$ booths:

Long tables: $300 \times 1 = 300$

Square tables: $300 \times 2 = 600$

Chairs for booths: $300 \times 4 = 1200$

Open space items:

Round tables: $75$

Chairs: $300$

Total chairs: $1200 + 300 = 1500$

Daily item rental:

Long tables: $300 \times 2 = \char36{}600$

Square tables: $\dfrac{600}{100} \times 30 = \char36{}180$

Round tables: $\dfrac{75}{5} \times 20 = \char36{}300$

Chairs: $\dfrac{1500}{50} \times 10 = \char36{}300$

Total item rental per day:
$600 + 180 + 300 + 300 = \char36{}1380$

4. Calculate total item rental and staff costs

Items are also rented for $4$ days.

Total item rental:
$1380 \times 4 = \char36{}5520$

Security guards:
$2 \times 12 \times 3 \times 10 = \char36{}720$

Part-timers:
$4 \times 12 \times 3 \times 8 = \char36{}1152$

Total staff cost:
$720 + 1152 = \char36{}1872$

5. Find the profit and compare it with the target profit

Total cost:
$53\,600 + 5520 + 1872 = \char36{}60\,992$

Profit:
$372\,000 - 60\,992 = \char36{}311\,008$

Since $311\,008 > 300\,000$, the organiser will meet the minimum target profit.