Beatrice is interested in consuming only in a fixed proportion: 2 units of good 1 and 4 units of good 2. The price of good 1 is 4, the price of good 2 is 3, and Beatrice's income is 30. (a) Please find the utility function that represents Beatrice's indifference curves, and draw an indiffer- ence curve on the -coordinate plane. (b) Please write down Beatrice's budget equation. If Beatrice spends all the income on good 1, how many units of good 1 could Ryan buy? How about Beatrice spends all the income on good 2? Please draw the budget line on -coordinate plane. (c) Please find Beatrice's optimal consumption bundle. (d) Please draw the income consumption curve. What is the slope of the income consumption curve? (e) Please draw the Engel curves of both goods. What are the slopes of them?