Petra consumes only two goods, pizza (P) and hamburgers (H) and considers them to be perfect substitutes, as shown by his utility function: U(P, H) = P + 4H. The price of pizza is $3 and the price of hamburgers is $6, and Paul's monthly income is $300.

a. Write the equation for Petra's budget line.

b. If hamburgers is on the vertical axis, what is the slope of the budget line?

c. Graph Petra's budget line. Place the hamburgers servings on the vertical axis and pizza on the horizontal axis. Make sure to indicate the values of where the budget line hits each axis.

d. On the same graph, draw several of Petra's indifference curves, including one that show where Petra will maximize his utility. Make sure to clearly indicate which indifference curve that maximizes utility.

e. Petra is a utility maximizer. Write down the full optimization problem with the objective function and the constraint.

f. Solve for the values of P and H that maximizes Petra's utility.