QUANTITATIVE ANALYSIS IN MANAGEMENT DECISIONA firm manufactures two products; the net profit on product 1 is Rupees 3 per unit and Rupees 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. (solve with graphical method)Use the graphical method to solve the LPPMaximize Z = 2X1 + 4X2Subject to constraints:X1 + 2X2 ≤ 5X1 + X2 ≤ 4And X1, X2 ≥ 0Write the dual of following problems:Maximize Z = 7X1 + 5X2Subject to:X1 + 2X2 ≤ 64X1 + 3X2 ≤ 12X1, X2 ≥ 0Maximize Z= 3X1 + 4X2Subject to:5X1 + 4X2 ≤ 2003X1 + 5X2 ≤ 1505X1 + 4X2 ≥ 1008X1 + 4X2 ≥ 80X1, X2 ≥ 0Determine initial basic feasible solution to the following transportation problem using the north west corner rule. D1D2D3D4AvailabilityO1641514O289271 6O343625Requirement61015435Obtain an initial basic feasible solution to the following transportation problem using Vogel’s approximation method. D1D2D3D4A513334B335415C644312D4-142 192125171780