Analyze the pricing structures for DJ Rain and DJ 5-Star, including calculating costs for different durations and representing them graphically.

The cost for DJ Rain is R4 000 for 5 hours or less. For more than 5 hours, there is an additional R1 250 per hour.
Let $C$ be the cost and $H$ be the number of hours. If $H > 5$, the cost is R4 000 for the first 5 hours plus R1 250 for each hour beyond 5 hours, which is $(H-5)$ hours.

From Table 4, DJ Rain costs R4 000 for 5 hours or less.

• For 3 hours, the cost is R4 000. So, $P = \boxed{\text{R}4\,000}$.
• For 6 hours, using the formula $C = 4000 + 1250(H - 5)$:

• For 9 hours, using the formula $C = 4000 + 1250(H - 5)$:

DJ 5-Star costs R1 000 per hour or part thereof. This type of pricing, where the cost jumps at whole hour intervals, is typically represented by a step graph.

To draw a line graph for DJ Rain using Table 5, you would plot the following points:
(1, 4000), (2, 4000), (3, 4000), (4, 4000), (5, 4000), (6, 5250), (7, 6500), (8, 7750), (9, 9000).
The graph would be a horizontal line from 1 to 5 hours at R4000, then a series of connected line segments from (5, 4000) to (6, 5250), then to (7, 6500), then to (8, 7750), and finally to (9, 9000).

First, calculate the duration DJ 5-Star is hired:
From 18:00 to 01:30 the next day is 7 hours and 30 minutes.
Since DJ 5-Star charges R1 000 per hour or part thereof, 7 hours and 30 minutes will be charged as 8 full hours.
Cost for DJ 5-Star = $8 \times \text{R}1\,000 = \text{R}8\,000$.

Now, sum all the budgeted expenses from Table 4 and the DJ cost:

• Cost of the venue: R750 (deposit) + R6 185 (for the day) = R6 935
• Food and drinks: R18 000
• Birthday cake: R1 250
• DJ 5-Star: R8 000

DJ Cool costs R6 000 for the party. DJ 5-Star costs R8 000 for the party (as calculated in 4.1.3).
Lee's parents chose DJ 5-Star, which is more expensive than DJ Cool.
One reason they might not have chosen DJ Cool is that DJ Cool may not have been available for the required time or may not have met their specific requirements for music or equipment.