2. Set up the appropriate linear program for each problem and Answer the following questions: a. Lawny Power makes two popular models of gasoline engines for lawn care equipment. The RKI weighs 16 Ibs, requires 4 hours of manufacturing time and 1 hour of assembly time. The RK2 weighs 24 lbs, requires 6 hours of manufacturing time, and 1.5 hours of assembly time. For the next production cycle, there are 1000 hours available for manufacturing and 650 hours available for assembly. Management wants to produce a total of at least 260 gasoline engines during the next production schedule. Lastly, there is a demand for at least 70 RK2 engines. i. The cost to produce one XK1 engine is $150 and to produce one XK2 engine is $120. 1. Use X1 and X2 as your decision variables. 2. (a) Write the LP formulation on your paper. 3. (b) Write the LP formulation in Standard Form directly below it. b. Poly-More Plastics is a subcontractor which fabricates the housing for air conditioning units of a major A/C company. Model A requires 13 lbs of moulded plastic and 9 hours of assembly time. Model B requires 19 lbs of moulded plastic and 8 hours of assembly time. For the next production period, there are 1100 lbs of moulded plastic and 580 hours of assembly time. There is a purchase order for at least 16 Model B housings. A second order for at least 13 Model A housings just came in i. The profit on each Model A housing is $45/unit and for the Model B housing is $65/unit. Develop an LP formulation to optimize the production schedule of A/C housings that will maximize the profit. 1. (a) Write the LP formulation. 2. (b) Write the LP formulation in Standard Form directly below it