can you please provide explanation and graphs

Sarah consumes only two goods, which can be divided into fractions: ap- ples (21) and books (12). Assume the price of books is p2 = 1. Suppose you know that, if she consumes 5 books, she can buy at most 10 apples. And if she consumes 8 books, she can buy at most 4 apples. (a) Determine her income (m) and the price of apples (p1). Write out the equation of her budget line. Draw this on a graph (clearly marking the axes and intercepts) and indicate her budget set. (b) Suppose the government taxes Sarah's apple consumption in the fol- lowing way: for each apple consumed, Sarah must pay a tax of t = . Write out the equation for her new budget line, and draw it on a graph. (c) After evaluating this policy, the government decides that the tax is too harsh. It now declares that the tax will kick in only after 5 apples. (If x1 5, the tax applies to each apple that exceeds this cutoff.) Sarah will now face a kinked budget line. Write the equations corresponding to each part of her budget line, and draw them on a graph (indicate the bundle at which the kink occurs). (d) This government is extremely indecisive. In another change of policy, it decides that the tax break makes sense for the poor, but there is no reason to offer it to the rich. The new policy is as follows: if a person's income is less than or equal to $10, she gets the tax break (as described in part c), but if her income is greater than $10, she must pay taxes on her entire purchase of apples (as described in part b). Now suppose Sarah's employer offers her a raise of $2. Can we be certain that Sarah will accept the raise? What about a raise of $4? Analyze this by thinking about how the budget set changes after each raise