Implement and solve the model using AMPL. Make sure that the model allows for changes in the data as well as the dimension (i.e., size) of the problem instance. Provide the .mod, .dat and .run files for the model.

All-Natural Cereals makes three breakfast cereals, A, B, and C, from four high-quality all- natural ingredients: rolled oats, raisins, shredded coconuts, and slivered almonds. The monthly availabilities of the four ingredients are 30 tons, 3 tons, 3 tons, and 3 tons, respectively (1 ton = 2000 pounds). The corresponding costs per ton are $1,500, $3,000, $2,700 and $4,000. Cereal A is a 50:7:3 mix of oats, raisins, and almonds, cereal B is a 50:7:3 mix of oats, coconuts, and almonds, while cereal C is a 9:1:1:1 mix of oats, raisins, coconut and almonds. The cereals are produced in large 2.5-lb bags. Cereals A, B, and C are sold for $4.75, $5.25 and $6.0 per bag, respectively. The monthly demand for the three cereal types is estimated at 15,000, 18,000 and 12,000 bags, respectively. Beyond the ingredient costs, an additional variable cost of $0.5 is incurred for preparing each bag of cereal. The following LP was formulated to determine the optimal production mix for the cereals and the associated required amounts of ingredients. 4.25w, +4.75 +5.5w -0.75y, -1.5y, -1.35y, -2y, Yo = X+X max s.t. Y = X + XC XtXt w = 0.4x +0.4.x, +0.4x w = 0.4x +0.4x +0.4x we=0.4x +0.4x +0.4x +0.4x 7xal = 50x, 3x = 50xat 7x8 = 50x8 3x = 50x Xoc=9xc x =9x x&c=9x y, 60,000 y, 6,000 y, $6,000 y, 6,000 w 15,000 A W 18,000 We 12,000 XXXCXXCXB XCX 4 XaXac 20 aC W Was We 20 and integer 45