SHOW ALL WORK. ZERO POINTS WILL BE EARNED FOR ANSWERS WITHOUT ALL WORK. 1. (4.3, p. 207): A small manufacturing plant makes three types of inflatable boats: one-person, two-person, and four-person models. Each boat requires the services of three departments as listed in the table. The cutting, assembly, and packaging departments have available a maximum of 350, 330, and 115 labor-hours per week, respectively. Construct a mathematical model for this problem. Use Gauss.Jordan elimination to solve the model and then interpret the solution (answer the questions). Department Cutting: Assembly: Packaging: 1-Person Boat 0.5 hr 0.6 hr 0.2 hr 2-Person Boat 1.0 hr 0.9 hr 0.3 hr 4-Person Boat 1.5 hr 1.2 hr 0.5 hr A) How many boats of each type must be produced each week for the plant to operate at full capacity? B) How is the production schedule in part (A) affected if the packaging department is no longer used? C) How is the production schedule in part (A) affected if the four-person boat is no longer produced