Question 1. LP formulation and Graphical method (12 pts) 1. A farmer has recently acquired a 110 hectares piece of land. He has decided to grow Wheat and barley on that land. Due to the quality of the sun and the region's excellent climate, the entire production of Wheat and Barley can be sold. He wants to know how to plant each variety in the 110 hectares, given the costs, net profits and labor requirements according to the data shown below: Variety Cost (Price/Hec) Net Profit (Price/Hec) Man-days/Hec Wheat 100 50 10 Barley 200 120 30 The farmer has a budget of SAR10,000 and availability of 1,200 man-days during the planning horizon. Formulate the LP model. 2. Solve the following LPP using the graphical method Minimize T = 3x + y S.t. x + 2y >=4 x + 3y >=6 x, y >=0 Question 2. Simplex Method (13 pts) 1. Solve the following problem using simplex method and check your result using the graphical method. Maximize z= 12 x1 + 16 x2 s.t. xl + 2 x2 =0 2. Solve the following minimization problem by solving its dual maximization problem with the simplex method and determine the values of xl and x2. Minimize w=29 x1 + 10 x2 s.t. 3 x1 + 2 x2 >= 2 5 x1 + x2 >=3 x1,x2 >=0