Question 1 Report
A community theatre stages a musical for six evenings. It pays $4,800 to hire the theatre and has other costs of $6 for each audience member. Tickets are sold at $18 each. The manager expects 500 people to attend in total.
(a) Calculate the theatre's total variable costs if 500 tickets are sold. [2]
(b) Calculate the total costs for the six performances. [3]
(c) Analyse whether the theatre will make a profit if it sells 500 tickets. [4]
(a) Variable costs change with output. The cost per audience member is $6, so for 500 ticket-holders:
\[500 \times \$6=\$3000\]
Total variable cost is $3000 [2].
(b) Total cost is fixed cost plus variable cost. Theatre hire is fixed for the six evenings, whereas the $3000 changes with attendance:
\[\text{Total cost}=\$4800+\$3000=\$7800\]
The total cost is $7800 [3].
(c) Profit is total revenue minus total cost. Revenue is ticket price multiplied by tickets sold:
\[\text{Total revenue}=500\times\$18=\$9000\]
\[\text{Profit}=\$9000-\$7800=\$1200\]
The theatre will make a profit of $1200 [4], because total revenue of $9000 exceeds total costs of $7800. Do not confuse revenue with profit: revenue is all ticket income before costs are deducted.
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