Aisha is considering how to allocate the next 6 hours of her free time. She could choose between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at 25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is 12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U(L,P)=3L+P. (MU_L=3,MU_P=1).

a. Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis.

b. Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained.

c. Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning.

d .Would Aisha's optimal choice change if she could get a discount on her pizza purchases so that each pizza would cost 5? Explain.

e.Would Aisha's optimal choice change (as compared to c), if she could get a discount on her pizza purchases so that each additional pizza beyond the first two, cost 5? (In other words, the first two pizzas need to be purchased at a regular price of 12.50 each, but the third, fourth, etc. can be purchased at a discounted price of 5). Explain.