A company manufactures organic juice and uses this demand function to determine the amount it should make at different prices: q=100−2p The revenue and expense functions are given by: R(p)=100p−2p^2 and E(p)=1,200−10p What is the profit equation P(p) in terms of price p ?
Answer
A
cap p times p is equal to 2 p squared plus 110 p minus 1 comma 200
B
cap p times p is equal to negative 2 p squared plus 100 p minus 1 comma 200
C
cap p times p is equal to 2 p squared plus 110 p plus 1 comma 200
D
cap p times p is equal to negative 2 p squared plus 110 p minus 1 comma 200
Explanation
Profit equals revenue minus expenses: P(p) = R(p) − E(p). Substituting the given functions gives P(p) = (100p − 2p²) − (1,200 − 10p) = −2p² + 110p − 1,200. This matches choice D, negative 2p squared plus 110p minus 1,200.
AI-written and checked against the verified answer.