I need steps and explanation for this

EXTRA CREDIT: Imagine a consumer spends his budget on good X and good Y. He has a utility function U = X /2Y1/2. The price of good X (Px) is $2, and the price of good Y (Py) is $2, and his budget (M) is $10. Use the method of Lagrange multipliers to calculate the optimal consumption bundle. a) Write the Lagrange equation. i) L = X1/2y1/2 - > (2X + 2Y - 10) b) Calculate all three first derivatives of the Lagrange equation. aL *-1/2 v1/2 - 21 ax aL x1/2 Y-1/2 - 21 aY 2 aL = 2X + 2Y - 10 C) Calculate the utility maximizing bundle. X = 2.5, Y = 2.5 d) Calculate the Lagrange multiplier. 2 = 0.25