At Atlantic Life Care (ALC) senior homes, they operate woodworking facilities. These serve as a way to get seniors engaged in 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. Cutting time Assembly Time Profit Chairs 2 hrs Tables 1 hr 3 hrs 2 hr $18 $12 Each chair will use 3 hockey sticks. Tables will require 6. They have 15 sticks. At the Bedford seniors' home, they have 26 hours for cutting and 50 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. [15 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. Q2. [29 pts] Consider the following LP model Minimize C = 14A + 20B Subject to 2A + 4B 200 2A + B 140 2A-B0 A, B0 a. [12 pts] Plot and label the constraints and feasible region. b. [17 pts] Identify all corner points, the optimal solution, and the optimal value.