Chloe's income is m = 600 and prices are p = 20 per unit of the first good and q = 30 per unit of the second

good. Chloe's preference for consumption bundles containing these two goods can be represented by the

utility function

u(x, y) = 2x (y+3)= 2xy + 6x,

where x is the quantity of good 1 and y is the quantity of good 2 in the consumption bundle (x, y).

1. What is the equation for Chloe's budget line (i.e. their "budget equation")?

2. Sketch Chloe's budget set (mark all important points).

3. Find Chloe's optimal consumption bundle (remember to check for interior and corner solutions).

Please give me the correct answer with explanation.