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The Hampshire Chemical Company must produce exactly 1,000 pounds of a special mixture of phosphate and potassium for a customer. Phosphate costs £5 per pound and potassium costs £6 per pound. No more than 300 pounds of phosphate can be used, and at least 150 pounds of potassium must be used. The problem is to determine the least-cost blend of the two ingredients.   (i) Formulate the problem with a linear programming model.   (ii) Solve for the optimal solution by using the simplex method.   (iii) How can you detect the presence of alternative optimal solutions from the final simplex tableau?

The Hampshire Chemical Company must produce exactly 1,000 pounds of a special mixture of phosphate and potassium for a customer. Phosphate costs £5 per pound and potassium costs £6 per pound. No more than 300 pounds of phosphate can be used, and at least 150 pounds of potassium must be used. The problem is to determine the least-cost blend of the two ingredients.   (i) Formulate the problem with a linear programming model.   (ii) Solve for the optimal solution by using the simplex method.   (iii) How can you detect the presence of alternative optimal solutions from the final simplex tableau?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 33E
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The Hampshire Chemical Company must produce exactly 1,000 pounds of a special mixture of phosphate and potassium for a customer. Phosphate costs £5 per pound and potassium costs £6 per pound. No more than 300 pounds of phosphate can be used, and at least 150 pounds of potassium must be used. The problem is to determine the least-cost blend of the two ingredients.

 

(i) Formulate the problem with a linear programming model.

 

(ii) Solve for the optimal solution by using the simplex method.

 

(iii) How can you detect the presence of alternative optimal solutions from the final simplex tableau?

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