1. Make sure to include the following steps/answers in you work and list by the following letters a) b) c) d) e) Define your variables. What does x represent, what does y represent? Find the objective function. Write a system of constraints. Use Desmos.com to graph the system of constraints and then sketch on your paper. Use the vertices/corners to find the number of American and British planes used to maximize cargo capacity. 2. Polly has made a commitment to exercise in order to lose weight and improve overall fitness. Polly would like to burn at least 3000 calories per week through exercise but wants to schedule at most 7 hours of exercise each week. Polly will do both running and weightlifting for exercise. Running burns 600 calories per hour and weightlifting burns 400 calories per hour. f) g) h) i) j) Define your variables. What does x represent, what does y represent? Find the objective function. Write a system of constraints. Use Desmos.com to graph the system of constraints and then sketch on your paper. Use the vertices/corners to find the weekly hours of running and weightlifting that will burn the maximum amount of calories. Also, identify how many calories she would burn. 3. Describe a situation in YOUR life in which you would really like to maximize something, but are limited by at least two constraints. Can linear programming be used in this situation? Explain your answer.