1 Study Time Sam is trying to allocate his study time this weekend. He can spend time working with either his math tutor or his accounting tutor to prepare for exams in both classes the following Monday. His math tutor charges $20 per hour, and his accounting tutor charges $40 per hour. He has $220 to spend on tutoring. Each hour that he spends working with his math tutor requires 1 aspirin and 1 hour of sleep to recover. Each hour that he spends with his accounting tutor requires half an aspirin and 3 hours of sleep to recover. The maximum dosage of aspirin that he can safely take during his study time is 8 tablets. He can only afford 15 hours of sleep this weekend. He expects that each hour with his math tutor will increase his score on the math exam by 3 points, while each hour with his accounting tutor will increase his score on the accounting exam by 5 points. How many hours should he spend with each tutor in order to maximize the number of points he will get on the two tests combined? 1 Solution 1. Step 1: Define the objective function and constraints. Clearly define your variables: x : y : Define an objective function based on these variables: Are the variables constrained to non-negative values? If so, include inequalities to represent this constraint: Write an inequality that represents the money constraint: Write an inequality that represents the aspirin constraint: Write an inequality that represents the sleep time constraint: 2 2. Step 2: Graph the solution set of the inequalities defined by the constraints. This graph should be neat use a straightedge, be consistent with scale, and label each line with its equation. You may use the space below, or you can use Desmos or other technology to create the graph; if you choose to do that, upload a screenshot of your graph along with your report. 3. Step 3: Find the location of the vertices and label them on the graph above. 3 4. Step 4: Evaluate the objective function at each of the vertices and record the results in the table below. Vertex Objective function value Conclusion How many hours should he spend with each tutor in order to maximize the number of points he will get on the two tests combined?