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Algebra, STD1 EQ-Bank 22

Gemstar Promotions is organising the annual Concert Under the Stars event to take place on the last weekend in January.

The outdoor venue holds up to 800 people. Each ticket holder receives a complimentary souvenir program valued at $15.

Garth from Gemstar Promotions uses a spreadsheet to model the costs and revenue for the concert. 
  

  1. What are the total fixed costs for the concert?   (1 mark)
  2. The promoter will only proceed with the concert if the loss is no more than $3000.   
  3. What is the minimum number of tickets that must be sold for the concert to go ahead?   (2 marks)
  4. Use the formula in cell C9 to calculate the number of tickets that must be sold for the promoter to break even?   (1 mark)
  5. Calculate the profit for Gemstar Promotions if the concert is fully booked.   (1 mark)
Show Answers Only

a.    \($30\,000\)

b.    \(450\ \text{people}\)

c.    \(500\ \text{people}\)

d.    \($18\,000\)

Show Worked Solution

a.    \(\text{Total fixed costs}=$8000+$6000+$16\,000=$30\,000\)
    

b.    \(\text{Maximum allowable loss}=$3000\)

\(\text{From the spreadsheet, at}\ 450\ \text{people}:\)

\(\text{Total cost}=$36\,750,\ \text{Revenue}=$33\,750\)

\(\text{Loss}=$36\,750-$33\,750=$3000\ \checkmark\)

\(\therefore\ \text{Minimum ticket sales}=450\)
  

c.    \(\text{Breakeven = C6/(C7-C8)}\)

\(\text{Breakeven}\ = \dfrac{30\,000}{75.00-15.00}=500\ \text{people}\)
  

d.    \(\text{Venue capacity}=800\ \text{people}\)

\(\text{Variable cost} =800\times \$15= $12\,000\)

\(\text{Total costs} =$30\,000+$12\,000= \$42\,000\)

\(\text{Revenue} =800\times \$75 = \$60\,000\)

\(\therefore\ \text{Profit} = \$60\,000-\$42\,000 = \$18\,000\)