A company produces two products ca-f and ch-f. They use three types of raw-materials, namely, 'C', 'L', and 'F'. The raw materials contain two main types of ingredients, namely, 'P' and 'A'. The following table gives the ingredients' contents in standard units per pound of each raw-material. Table 1: Composition Ingredients/Raw-materials P 27 A 20 L F 20 30 30 20 The 'P' ingredient must lie in the interval [22, 25) per pound of ca-f. Also the 'A' content must be greater than or equal to 22 per pound of the ca-f. Similarly, the 'P' ingredient and the A ingredient must be in the intervals (21, 24) and (21, 29), respectively, per pound of the ch-f. Suppose that 3000, 2500, and 1000 pounds of 'C', 'L', and 'F', respectively, are available. Also, suppose that it is required to produce 4000 and 2000 pounds of ca-f and ch-f, respectively. Let the price per pound of 'C', 'L', and 'F' be respectively $0.20, $0.15, and $0.25. [5 Points] (a) Formulate the blending problem with an objective of minimizing the cost. (10 Points] (b) Formulate the problem using Dantzig-Wolfe decomposition technique using two convexity constraints, state the master and sub-problem(s). [10 Points] (c) Perform two iterations for the decomposition. [5 Points] (d) Extra corn and fish meal can be obtained but, because of shortages, at the higher prices of $0.22 and $0.27 per pound. Would you advise the mill to consider extra corn and fish meal and modify their blending at these prices? Why or why not? A company produces two products ca-f and ch-f. They use three types of raw-materials, namely, 'C', 'L', and 'F'. The raw materials contain two main types of ingredients, namely, 'P' and 'A'. The following table gives the ingredients' contents in standard units per pound of each raw-material. Table 1: Composition Ingredients/Raw-materials P 27 A 20 L F 20 30 30 20 The 'P' ingredient must lie in the interval [22, 25) per pound of ca-f. Also the 'A' content must be greater than or equal to 22 per pound of the ca-f. Similarly, the 'P' ingredient and the A ingredient must be in the intervals (21, 24) and (21, 29), respectively, per pound of the ch-f. Suppose that 3000, 2500, and 1000 pounds of 'C', 'L', and 'F', respectively, are available. Also, suppose that it is required to produce 4000 and 2000 pounds of ca-f and ch-f, respectively. Let the price per pound of 'C', 'L', and 'F' be respectively $0.20, $0.15, and $0.25. [5 Points] (a) Formulate the blending problem with an objective of minimizing the cost. (10 Points] (b) Formulate the problem using Dantzig-Wolfe decomposition technique using two convexity constraints, state the master and sub-problem(s). [10 Points] (c) Perform two iterations for the decomposition. [5 Points] (d) Extra corn and fish meal can be obtained but, because of shortages, at the higher prices of $0.22 and $0.27 per pound. Would you advise the mill to consider extra corn and fish meal and modify their blending at these prices? Why or why not