Question 5. You have just read an article that suggests that successful performance on exams requires two things: studying and rest. Neither by itself produces good exam grades but in the right combination, they maximize exam performance. You wonder what that combination is for yourself. You decide that exam grades are the "output\" that comes from a production process that takes two inputs: hours of studying and hours of rest. This production process satisfies the condition of diminishing marginal product of both inputs. 5.1. Draw a set of axes with hours of study, S, on the horizontal axis, and hours of rest, R, on the vertical axis. Put an isoquant that represents a particular exam grade XA. Label the isoquant "lsoquant." 5.2. Suppose you are always willing to pay $5 to get back an hour of rest, and $10 to get back an hour of studying. These would therefore be the prices of the two inputs. Illustrate on your graph the least cost way to get to the exam grade XA. Put the slope of any curve you draw, if you can find it. (Note that you're not expected to find specific numbers for the cost-minimizing bundle. Just label the picture to make it clear where that bundle is.) Suppose you are not very satisfied with a graphical approach to your answer, and you decide to find the optimal combination of study and rest mathematically. You posit that your production function for exam grades looks like this: X = 40(5)(R)i Where X is your exam grade, S is the number of hours spent studying and R is the number of hours spent resting. Again, just as above, you are always willing to pay $5 to get back an hour of rest, and $10 to get back an hour of studying. 5.3. Find the optimal relationship between S and R that you should use if you were cost minimizing. 5.4. Suppose that you decide that you wanted to get X = 80 on your exam. What combination of S and R that will achieve this grade with the lowest cost? Use a scientific calculator if you need to. 5.5. Describe in words what would happen to your optimal input choice if the cost of an hour of studying went up (that would happen if, for instance, studying got significantly more complicated or burdensome)