A student is taking an exam consisting of 10 essay questions and 50 short-answer questions. They have 90 minutes to take the exam and know they cannot possibly answer every question. The essay questions are worth 20 points each, and the short-answer questions are worth 5 points each. An essay question takes 10 minutes to answer, and a short-answer question takes 2 minutes. The student must do at least 3 essay questions and at least 10 short-answer questions.
(a) Fill in the following chart.

(b) Let x be the number of essay questions to be answered and y be the number of short-answer questions to be answered. Refer to the chart, and give the inequality that x and y must satisfy due to the amount of time available.
(c) Give the inequalities that x and y must satisfy because of the numbers of each type of question and also because of the minimum number of each type of question that must be answered.
(d) Give an expression for the total score obtained from answering x essay questions and y short-answer questions.
(e) Graph the feasible set for the exam strategy problem.

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Short- Answer Questions Questions Available Essay Time to answer Quantity Required Worth