The Southfork Feed Company makes a feed mix from four ingredients: oats, corn, soybeans, and a vitamin supplement. The company has 300 pounds of oats, 400 pounds of corn, 200 pounds of soybeans, and 100 pounds of vitamin supplement available for the mix. The company has the following requirements for the mix: 1] At least 30% of the mix must be soybeans. 2] At least 20% of the mix must be the vitamin supplement. 3] The ratio of corn to oats cannot exceed 2 to 1. 4] The amount of oats cannot exceed the amount of soybeans. 5] The mix must be at least 500 pounds. A pound of oats costs $0.50; a pound of corn, $1.20; a pound of soybeans, $0.60; and a pound of vitamin supplement, $2.00. The feed company wants to know the number of pounds of each ingre- dient to put in the mix in order to minimize cost. Here is the formulation: x1 is oats, x2 is corn, x3 is soybean and x4 is vitamin supplement minimize .50x1 +1.20x2 + .60x3 + 2.00x4 subject to x1 <= 300 x2 <= 400 x3 <= 200 x4 <= 100 -.3x1-.3x2 +.7x3.3x4 >= 0 -.2x1.2x2 .2x3 +.8 x4 >= 0 x22x1 <= 0 x1 x3 <= 0 x1 + x2 + x3 + x4 >= 500 Global optimal solution found. Objective value: Infeasibilities: Total solver iterations: Elapsed runtime seconds: Model Class: Total variables: Nonlinear variables: Integer variables: e +00 420.0000 0.000000 3 0.12 LP Total constraints: 10 Nonlinear constraints: Total nonzeros: Nonlinear nonzeros: 24 е Variable x1 Value 200.0000 Reduced Cost 0.000000 x2 0.000000 0.000000 хз 200.0000 0.000000 X4 100.0000 0.000000 Row slack or Surplus Dual Price 1 420.0000 2 100.0000 3 400.0000 4 0.000000 5 0.000000 6 50.00000 7 0.000000 8 400.0000 9 10 0.000000 0.000000 -1.000000 e.eeeeee oats constraint e.eeeeee corn constraint 1.300000 Soybeans constraint e.eeeeee vitamin constraint 0.000000 At least 30% soybeans -0.seeeeee At least 20% vitamin e.eeeeee corn to oats ratio 0.7000000 Oats cannot exceed soybeans -1.360000 Mix must be at least 500 lbs Ranges in which the basis is unchanged: Objective Coefficient Ranges: Current Allowable Allowable Variable Coefficient Increase Decrease x1 0.5000000 0.7000000 INFINITY x2 1.200000 0.8000000 0.6500000 X3 X4 0.6000000 2.eeeeee 1.300000 INFINITY INFINITY 0.8000000 Righthand side Ranges: Allowable Allowable Current ROW RHS Increase Decrease 2 300.0000 INFINITY 3 400.0000 INFINITY 100.0000 Oats constraint 400.0000 Corn constraint 4 200.0000 0.000000 5 100.0000 INFINITY 6 0.000000 50.00000 7 0.000000 0.000000 8 0.000000 INFINITY 9 0.000000 0.000000 10 500.0000 0.000000 50.00000 soybeans constraint 0.000000 vitamin constraint INFINITY At least 30% soybeans 100.0000 At least 20% vitamin 400.0000 Corn to oats ratio 133.3333 Oats cannot exceed soybeans 0.000000 Mix must be at least 500 lbs