text: The previous answer is correct, however, you can get it much easier by applying calculus.\n\nAs stated by the previous poster, \n\nR = QP = 10000P - 1.25 P^2\n\nThis function will have a maximum where its slope, (more properly, the slope of its tangent line) = 0.  That is, when a change in price causes the change in revenue to go from positive to negative, that's where revenue is highest.  Thus, we want\n\ndQ/dP = 0\n\ndQ/dP = 100,000 - 2 (1.25)P\n\n0 = 100,000 - 2.5P\n100,000 = 2.5 P\n\nP = 40,000.