The question is below. I need d and e answer.

[Utility Maximization] Mary spends her income on housing (H) and food (F). Her utility function is given by: U(H, F) = 3HF - H + F income is $9. Suppose the price of food is $1 per unit and the price of housing is $2 per unit. Assume her a) Write down Mary's budget constraint and find the expression for her marginal rate of substitution (MRS HF). b) Assume the optimal choice of (H*,F*) is not a corner solution. Write the equation that represents the tangency between Mary's budget constraint and her indifference curve. c) Find the optimal quantity of housing (H*) and all other goods (F*).d) Suppose Mary's income increased from $9 to $11 1What are her new choice of H" and F"? e) Suppose in addition to her income, Many receives a sulosidjpr of $10 that she can only;r spend on housing. What are Mary's netsr choice of H" and F"