Please answer Elements of Mathematical Economics.

5. P5: Lagrange Multiplier Method a. Consider the following utility function: U=X4Y4,x,y>0. Let Px=2 and Py=3 and M=100. Find the utility-maximizing consumption bundle. b. Find the marginal utilities of the goods, x and y. Are they always positive? c. Sketch their graphs. d. By implicit differentiation, find the slope of any difference curve and show that it is given by the ratio of marginal utilities of the two goods.Are the indifference curves always negatively sloped? Sketch their graphs. 6. For what kinds of goods might a consumer have upward sloping demand curves? Explain