A consumer's utility function is u = 10X0.2 + Y0.8

a. Derive the marginal utility functions for goods X and Y, and the marginal rate of substitution

b. Assume that a consumer has 3 units of good X and 5 units of good Y

c. Calculate the change in utility associated with an additional unit of X, all else equal.

d. How many units of good Y is this consumer willing to give up for an additional unit of X, while the total utility is held constant?