Start by solving the problem using allowance Z in place of 288 and prices Px and Py in place of 6 and 6. I get the multiplier Z/PxPy and solutions X = Z/2Px, Y = Z/2Py. The maximum utility is U = 2XY = Z^2/2PxPy. To answer (c), solve for Z satisfying Z^2/2x8.64x6 = 288^2/2x6x6, which is the initial maximum utility. The required Z = 288 x sqrt(8.64/6).