Final answer:
After calculating the profit for each given price by substituting into the profit equation P = -400p^2 + 12,400p - 50,000, we determined that none of the options (A through E) provided the correct profit figure.
Step-by-step explanation:
The student's question deals with a profit equation P = -400p^2 + 12,400p - 50,000, and the student is tasked with identifying which of the given price-profit pairs (A-E) could possibly satisfy this equation. We'll calculate the profit for each given price by substituting the price into the equation and comparing the result with the provided profit.
For option A: P = -400(6)^2 + 12,400(6) - 50,000 = -400(36) + 74,400 - 50,000 = 14,400 + 24,400 - 50,000 = 38,800 (not 10,000, so A is incorrect).
For option B: P = -400(8)^2 + 12,400(8) - 50,000 = -400(64) + 99,200 - 50,000 = 25,600 + 49,200 - 50,000 = 74,800 (not 34,000, so B is incorrect).
For option C: P = -400(12)^2 + 12,400(12) - 50,000 = -400(144) + 148,800 - 50,000 = 57,600 + 98,800 - 50,000 = 156,400 (not 45,200, so C is incorrect).
For option D: P = -400(18)^2 + 12,400(18) - 50,000 = -400(324) + 223,200 - 50,000 = 129,600 + 173,200 - 50,000 = 302,800 (not 43,600, so D is incorrect).
For option E: P = -400(20)^2 + 12,400(20) - 50,000 = -400(400) + 248,000 - 50,000 = 160,000 + 198,000 - 50,000 = 358,000 (also not 38,000, so E is incorrect).
Therefore, none of the provided options A through E correctly match the profit that would be calculated using the profit equation.