4. It is exactly 24 hours before Daryl's exams, and she is going to spend the entire time studying. She has an Economics exam followed directly by a Biology exam, with no time to study in between. Daryl's utility is represented by U(c,b} = (32 - l;- where c is the score on the Economics exam and l: is the score on the Biology exam. Daryl wants to be an economist, so she places more weight on her Economics exam score it has a higher exponent in her utility function, 2 instead of 1. Although Daryl cares more about Economics, she is better at Biology. Specically, for each hour spent studying Biology, she will increase her score by 5 points, but her Economics score will only increase by 3 points for every hour spent studying Economics. Before studying, she starts at a score of [i for each test. [a] We often write budget equations in the form PXI+PYIIE M: with px, py indicating prices of goods X and Y; 3:, 3; indicating quantities of those goods; and M indicating the total budget to be spent. Let's write a budget equation for this problem. Say Daryl will spend in; hours studying economics and .313 hours studying biology out of her 24 total hours. Write out the budget equation describing the possible values of h e and in; that Daryl can choose. Explain what it means that the \"prices\" of fig and fig the coeicients in front of them are both equal to 1 in this equation. (b) We can also write Daryl's budget equation in terms of test scores rather than hours. Rewrite your budget equation from the previous question in terms of e and 5 [instead of fig and .513) by plugging in the relationships c = 3kg and = 5kg. Once again, we can think of the coefcients in front of c and ii as representing \"prices\