Draw the indifference curve and the budget line

1. Thomas consumes only pizzas (Z) and burritos (B). His utility function is given by
U(Z, B) = Z · B.
The price of a pizza is pZ and the price of a burrito is pB. Thomas has Y dollars.
(a) Draw Thomas’s indifference curves and budget line if pZ = 20, pB = 10, Y = 100.
(b) Find the optimal amount of pizzas and burritos Thomas will buy if pZ = 20,
pB = 10, Y = 200.
(c) Derive Thomas’s demand function for pizzas if pB = 5 and Y = 5.
(d) Is Thomas better off if i) pizzas and burritos become twice cheaper, or if
ii) his income doubles?
(e) Suppose Thomas enters a cafeteria and discovers that pZ = 10 and pB = 25
(burritos are really delicious there). Thomas has Y = 200 in his pocket and
would like to make an optimal choice. However, he is told that there are only
two burritos left. Draw the budget constraint and find the optimal consumption
bundle.
2. Thomas consumes only beer (B) and Internet (I). He subscribes to an Internet provider
that charges 2 dollars per hour; the price of beer is pB = 1. Thomas has Y = 100
dollars to spend and is at equilibrium by optimally buying 10 hours of Internet access
and 80 cans of beer. Draw the indifference curve and the budget line. If the company
switches to a 20 dollars monthly flat fee for unlimited Internet access, is Joe better
off? Explain.