43. The Southwest Foods Company produces two brands of chili-Razorback and Longhorn from several ingredients, including chili beans and ground beef. The number of 100-gallon batches of Razorback chili

  

43. The Southwest Foods Company produces two brands of chili-Razorback and Longhorn from several ingredients, including chili beans and ground beef. The number of 100-gallon batches of Razorback chili (xi) and Longhorn chili (x2) that can be produced daily is constrained by the avail ability of chili beans and ground beef, as shown in the following linear programming model: maximize Z = 200 + 300X2 (profit, $) subject to 10×1 + 50×2 500 (chili beans, lb.) 34x 20×2 S 800 (ground beef, Ib.) xi,X2 2 0 The final optimal simplex tableau for this model is as follows: 200 300 Basic Variables Quantity 17/750-1/150 300 200 1/30 70/15 -310/75-70/15 20 5,800 200 300 310/75 0 PROBLEMS A-55 a. Formulate the dual of this model and indicate what the dual variables equal. b. What profit for Razorback chili will result in no production of Longhorn chili? What will the new optimal solution values be? c. Determine what the effect will be of changing the amount of beans in Razorback chili from 10 pounds per batch to 15 pounds per batch. d. Determine the optimal ranges for c and c2 e. Determine the feasible ranges for qi (pounds of beans) and q2 (pounds of ground beef) f. What is the maximum price the company would be willing to pay for additional pounds of chili beans, and how many pounds could be purchased at that price? or ground beef, which should it be? instead of $300, would the optimal solution be affected? g. If the company could secure an additional 100 pounds of only one of the ingredients, beans h. If the company changed the selling price of Longhorn chili so that the profit was $400

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