Question 18 • Mathematics for Data and Financial Literacy
A tax preparation company provides tax returns as a service and uses this demand function to determine the number of clients q they will get at different prices: q=150−3p - The revenue function is given by: R(p)=p⋅q=150p−3p^2 - The expense function is given by: E(p)=500+10q=500+10(150−3p)=500+1,500−30p=2,000−30p What is the profit equation P(p) in terms of price p ?
Answer
A
cap p times p is equal to 150 p minus 3 p squared minus 2 comma 000
B
cap p times p is equal to 120 p minus 3 p squared minus 2 comma 000
C
cap p times p is equal to 210 p minus 3 p squared minus 2 comma 000
D
cap p times p is equal to 180 p minus 3 p squared minus 2 comma 000
Explanation
Profit equals revenue minus expenses. Subtract the expense function from the revenue function: P(p) = (150p − 3p²) − (2,000 − 30p) = 150p − 3p² − 2,000 + 30p = 180p − 3p² − 2,000. This matches choice D.
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