Suppose that a consumer's utility is given by , in which case the marginal utilities will be given by and , respectively. Given arbitrary prices for good x, good y, and income (P x P , and I, respectively), solve for the consumer's demand for good x. That is, your final equation should have the optimal value of x on the left hand side, and some combination of P , P , and / on the right hand side. X y O I . P y 25 / P 2 , or, simplified, x = - P P + 25( P 2 X x y x P + P y O X= - P XO I . P 1= - , or, simplified, x = - 2 PP + P X X y X P + P y O I . P X 1= - , or, simplified, x = - P 2 PP + P 2 X y P + P