Andy consumes two goods: food (measured in dollars) and other things (also measured in dollars). Let x1 be the amount that Andy spends on food in a given month and let x2 be the amount that Andy spends on other things in a given month. Andy's preferences over consumption bundles (x1, x2) are summarized by the utility function:

u(x1, x2) = (x1)^3.(x2)^4

Andy's monthly income is $400.

1. What is Andy's optimal consumption bundle? Show your work. Illustrate Andy's budget line.

2. Suppose now that the government implements a subsidy program for food. Specifically, for each dollar that Andy spends on food, the government will give Andy $0.50. What is Andy's new optimal consumption bundle? Show your work. Illustrate Andy's new budget line.

3. The total amount of cash that Andy receives from the government cannot exceed $100. In a neat and clear diagram, graph Andy's budget line.