1. [43 pts] At Atlantic Life Care (ALC) senior homes, they operate woodworking facilities. These serve as a way to get seniors engagedlin productive and sometimes creative activities that generate financial benefits for the residents. The seniors make products that are sold to the public and the profits are returned to the residents, not ALC. They have recently received a donation of used hockey sticks that they will incorporate into the making of outdoor patio furniture. They plan to use them in two products: chairs and small tables. Chairs Tables Cutting time 3 hrs 1 hr Assembly Time 4 hrs 2 hrs Profit $20 $16 Each chair will use 2 hockey sticks. Tables will require 5. They have 10 sticks. At the Bedford seniors home, they have 24 hours for cutting and 48 hours for assembly. There should be at least 2 chairs for every table produced. a) [12 pts] Formulate an LP model to determine how many of each product should be made such that profit is maximized. b) [14 pts] Plot and label all the constraints and the feasible region. c) [17 pts] Identify all corner points, the optimal solution, and the optimal value