(Solved): The following table shows the marginal utility for each of six units of \( X \) and \( Y \). The p ...

The following table shows the marginal utility for each of six units of \( X \) and \( Y \). The price of \( X \) is \( \$ 4 \) and the price of \( Y \) is \( \$ 2 \). a. Suppose that the consumer's income is \( \$ 20 \). Assuming that the consumer is a utility maximizer, use marginal analysis to determine the optimal consumption of good \( x \) and good \( y \), respectively. Show your work. b. Suppose that the consumer instead has \( \$ 26 \) to spend. Assuming that the consumer is a utility maximizer, use marginal analysis to determine the optimal consumption of good \( x \) and good \( y \), respectively. Show your work.