given: Where: U(g,f) = utility function of consumer (U = g2/3 * f1/3 ), g = gasoline consumed, f = food consumed, = Lagrange multiplier, pg = price of gas ($2/liter), pf = price of food ($2/unit), M = consumer income ($150). : solve for f and g using these equations: (pg/pf) = (f/g)() and (L/) = M - pg(g) - pf(f)= 0