QUESTION 1 Total: 25 Marks Fresh Farms is into organic farming and has 200 acres of farmland in Cameron Highlands, which is suitable for cultivating crops. The costs for cultivating crops X1, X2, and X3 are RM40, RM50 and RM30 per acre respectively. Fresh Farms has a maximum of RM18,000 as funds for crop cultivation. Crops, X1, X2, and X3 require 20, 30 and 15 hours of labour per acre respectively, and the maximum number of labour hours available are 4,200. The farm expects to make a profit of RM70, RM90 and RM50 per acre on crops X1, X2 and X3 respectively. a) Formulate the given problem as a Linear Programming Problem. 17 marks b) Set up the initial simplex tableau by including the necessary slack variables. [4 marks] Given the following final table: 0 0 0 50 . Si S2 S3 Quantity C 70 90 Solution X2 Mix 70 Xi 1 0 0 S2 0 0 90 X2 0 1 Z 70 90 C-Z; 0 0 Si-slack for land constraint S2-slack for the budget constraint S; - slack for labor constraint 1.5 -5 -0.5 60 -10 3 -20 -2 30 -30 0 1 0 0 0 -0.1 --1 0.1 2 -2 180 9,800 20 14400 c) What is the optimal solution and the maximum value? [4 marks] d) What are the shadow prices of the three constraints and explain what do they mean? [4 marks e) Over what range can the profit contribution of crop X2 vary before a new solution point becomes optimal? marks 1) Determine the range for the right-hand side of the third constraint without changing the dual price. [2 marks