(PLEASE SHOW HOW TO DO STEP BY STEP #9 WITH DESMOS GRAPHING)

Anita is a competitive student whose goal is to maximize her GPA over the Spring quarter. She is enrolled in two classes and must decide on her study plan for the quarter. Specifically, she needs to figure out how much effort to dedicate to each class. The effort is counted in hours of work per week. We denote by ?? the effort devoted to class ? and by ?? the effort devoted to class ?. Anita's success in each class is an increasing function of the effort devoted to the class at low levels of effort, but as the overall study effort becomes large, she becomes tired and her performance decreases, harming her GPA. Mathematically, Anita's GPA for a quarter can be represented by the following differentiable function of ?? and ??:

w | e T e T F+2\\f_ M. . What will Anita's GPA be if she studies one hour per week for each class? . What will Anita's GP'A be if she studies one hour for class A and four hours for class B? Explain why, even though she devotes more time to class B in this case, her overall GPA is lower than in part 1. . What will Anita's GPA be if she studies four hours for class A and one hour for class B? . Using the expression for Anita's GPA, explain in words why she should devote more time to class A than class B. Write down the maximization problem that Anita must solve using the mathematical formu- lation introduced in lecture. Be sure to indicate Anita's choice variables. . Calculate the gradient of the GPA function at the effort levels (, ep). Find the optimal efforts }, and }, that Anita must consent to maximize her GPA. You may use a calculator to give a numerical approximation, but show your derivations. Find the maximized value of Anita's GPA. Using the graphing software of your choice, graph Anita's GPA function and check that your numerical answers to parts 7 and 8 are consistent with the graph. Make sure you select the relevant range of values for the domain of the function. Attach the graph to your answer sheet