Linear Programmng : Maximizing Profits
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Maximize P = x1 + 2x2 + 3x3 using the simplex method.
subject to the constraints
2x1 + x2 + x3 < 25
2x1 + 3x2 + 3x3 < 30
x1 > 0, x2 > 0, x3 > 0,
A company makes three products, A, B, and C. There are 500 pounds of raw material available. Each unit of product A requires 2 pounds of raw material, each unit of product B requires 2 pounds of raw material, and each unit of product C requires 3 pounds. The assembly line has 1,000 hours of operation available. Each unit of product A requires 4 hours, while each unit of products B and C requires 5 hours. The company realizes a profit of $500 for each unit of product A, $600 for each unit of product B, and $1,000 for each unit of product C. Formulate (but don't solve) a linear program to determine how many units of each of the three products the company should make to maximize profits.
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Solution Summary
A LP problem is solved using the simplex method. The solution is detailed and well presented.
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