John Has Two Midterm Exams-One in English and the Other $80 \%$

Essay

John has two midterm exams-one in English and the other in Introduction to Business-coming up exactly 4 days from now. He figures that he has a maximum of 30 hours that could be spent preparing for these exams. For every hour spent on English he expects to get 5 points. For every hour spent on Introduction to Business he expects to get 6 points. He needs to score a minimum of 50 points in English. He does not have to get more than 84 points in Introduction to Business to hit his target grade. He values the score he gets in English at $80 \%$ of the value he assigns to Introduction to Business. Formulate a linear program that maximizes the sum of properly weighted scores in both midterms, while satisfying the constraints. Solve the problem using the graphical method.