ECON 4510 Assignment 3 – Consider a consumer with utility

Assignment 3 ECON 4510/01 Microeconomics100 Points,To get full credit for your homework, it should be accurate, neat, and concise.Consider a consumer with utility function U = X1/2 + Y1/2 with an income of $120 to spend on good X (withprice $4) and good Y (with price $2).1 [10 points] Carefully express this consumer’s utility maximization problem, using the particulars of thisproblem.2 [40 points] Give two conditions that the consumer’s optimal bundle will satisfy, again using the particularsof this problem.3 [30 points] Solve these two conditions for the consumer’s optimal bundle. Neatly show your work.4 [20 points] Solve for the demand function for good X for a consumer with the given utility function. Inother words, resolve this problem only now leaving the prices and income as variables: pX, pY, and m.Neatly show your work.