Problem

Revenue is \(R=-p^{2}+12p\) for \(p\ge~0\), with target \(R=20\). Form and solve the system, keep every admissible price, write correctly ordered points, interpret them, and compare with the displayed answer graph.

Answer choices

Choose your path.

Preview only

System: R = −p² + 12p and R = 20. Set equal: −p² + 12p + 20 = 0, so p² − 12p − 20 = 0. Inputs 6 ± 2√14 give points (6 − 2√14, 20) and (6 + 2√14, 20): these are claimed target prices.

System: R = −p² + 12p and R = 20. Set equal: −p² + 12p = 20, so p² − 12p + 20 = 0. Inputs 2 and 10 give points (20, 2) and (20, 10): revenue and price are reversed.

System: R = −p² + 12p and R = 20. Set equal: −p² + 12p = 20, so p² − 12p + 20 = 0. Input 6 gives point (6, 20): the vertex price is the only target price.

System: R = −p² + 12p and R = 20. Set equal: −p² + 12p = 20, so p² − 12p + 20 = 0 = (p − 2)(p − 10). Inputs 2 and 10 give points (2, 20) and (10, 20): both prices yield 20 dollars of revenue.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Revenue is \(R=-p^{2}+12p\) for \(p\ge~0\), with target \(R=20\). Form and solve the system, keep every admissible price, write correctly ordered points, interpret them, and compare with the displayed answer graph.

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.