Year 11 is making pizzas to raise money for a charity - HSC - SSCE Mathematics Standard - Question 14 - 2024 - Paper 1
Question 14
Year 11 is making pizzas to raise money for a charity.
The cost (C) and revenue (R), in dollars, when x pizzas are sold are represented by the equations
C = 2.5x +... show full transcript
Worked Solution & Example Answer:Year 11 is making pizzas to raise money for a charity - HSC - SSCE Mathematics Standard - Question 14 - 2024 - Paper 1
Step 1
Calculate Revenue for x Pizzas Sold
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Answer
The revenue R when x pizzas are sold is given by the equation:
R=8x
This means that for every pizza sold, the revenue increases by $8.
Step 2
Calculate Cost for x Pizzas Sold
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Answer
The cost C when x pizzas are sold is given by the equation:
C=2.5x+6
This shows that the cost increases by 2.50foreachpizza,inadditiontoafixedcostof6.
Step 3
Determine Profit
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Answer
To find the profit P, we subtract the cost from the revenue:
P=R−C
Substituting the equations for R and C:
P=(8x)−(2.5x+6)=8x−2.5x−6
This simplifies to:
P=5.5x−6.
Step 4
Calculate Increase in Profit for Each Additional Pizza
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Answer
The increase in profit for each additional pizza sold is found by taking the derivative of the profit function or analyzing the profit for selling one more pizza:
Since profit is given by the formula above, the increase for each additional pizza is simply the change in profit:
Increase in Profit = Change in Revenue - Change in Cost = 8−2.50 = $5.50.
Thus, the profit increases by $5.50 for each additional pizza sold.
