[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 (MRSHF). 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 $17. What are her new choice of H* and F*? e) Suppose in addition to her income, Mary receives a subsidy of $10 that she can only spend on housing. What are Mary's new choice of H* and F*