Suppose A utility function U(x) = {ax{ +(1-)x2} with a > 0 and p>0 is defined...

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Suppose A utility function U(x) = {ax{ +(1-)x2}" with a > 0 and p>0 is defined over the set S = {(x) | xp+x2P2 M} where P, P2 are prices. Prove that if P1, P2 and M are positive, there exists at least one utility maximizing level of consumption of (x, x). Suppose A utility function U(x) = {ax{ +(1-)x2}" with a > 0 and p>0 is defined over the set S = {(x) | xp+x2P2 M} where P, P2 are prices. Prove that if P1, P2 and M are positive, there exists at least one utility maximizing level of consumption of (x, x).