B and C. please follow the hint.

(1) Consider a consumer with the utility function u(x, y) = xy. The consumer's income m = 100, and initial prices and p1 = 1 and p2 = 1. (a) Solve the consumer's utility maximization problem and draw a graph showing the budget line, the optimal bundle, and the indifference curve going through the optimal bundle. (b) Suppose the price of good 1 changes to pi = 2. Mathematically derive the income and substitution effects of this price change on consumption of good 1. (Hint: solve both the utility maximization problem for the new budget constraint and the expenditure minimization problem with the new prices and the previous level of utility.) (c) Draw a graph showing the income and substitution effects from in the previous