You need to solve the following equation:
-0.5x^2 +36x -161 = 451
Set right side to 0
-0.5x^2 +36x -612 = 0
Multiply by -2 to get rid of decimal and leading neg coefficient.
x^2 -72x + 1224 = 0
Use quadratic formula:
a = 1, b = -72, c = 1224
Therefore the min price to have 451 profit is $27.51
-0.5x^2 +36x -161 = 451
Set right side to 0
-0.5x^2 +36x -612 = 0
Multiply by -2 to get rid of decimal and leading neg coefficient.
x^2 -72x + 1224 = 0
Use quadratic formula:
a = 1, b = -72, c = 1224
Therefore the min price to have 451 profit is $27.51