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Algebra, STD1 EQ-Bank 16

A cafe owner uses a spreadsheet to model the costs and revenue from selling cups of coffee.

The cafe has a fixed setup cost of $450 and a cost per cup 0f $1.50 to make each coffee. The owner sells each coffee for $4.50.

Part of the spreadsheet is shown.
  

  1. What does it mean for the cafe owner to break even?   (1 mark)

  2. Use the spreadsheet to identify the break-even point for the cafe owner.   (1 mark)

  3. If the cafe owner sells 250 cups of coffee, what profit is made?   (2 marks)

Show Answers Only

a.    \(\text{Break-even is when the total cost equals the revenue}\)

\(\text{i.e. the owner makes neither a profit nor a loss.}\)

b.    \(150\ \text{cups}\)

c.    \($300\)

Show Worked Solution

a.    \(\text{Break-even is when the total cost equals the revenue}\)

\(\text{i.e. the owner makes neither a profit nor a loss.}\)
  

b.    \(\text{From the spreadsheet, total cost equals revenue when }\)

\(\text{Cost}=\text{Revenue}=$675\)

\(\therefore\ \text{Cups sold to break-even} = 150\)

\(\text{Confirmed by cell C15:}\)

\(\text{Break-even (cups)}=\dfrac{450}{4.50-1.50}=\dfrac{450}{3}=150 \text{ cups}\)
  

c.    \(\text{At 250 cups (row 9): Revenue} = \$1125,\ \text{Total cost} = \$825\)

\(\therefore\ \text{Profit} = 1125-825 = \$300\)