Maximization by the simplex method Solve the following linear programming problems using the simplex method. 1>. Maximize z =...

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Maximization by the simplex method
Solve the following linear programming problems using thesimplex method.
1>.
Maximize z = x₁ + 2x₂ +3x₃
subject to x₁ + x₂ +x₃ ? 12
2x₁ + x₂ + 3x3 ? 18
x₁, x_2, x₃ ? 0
2>.
A farmer has 100 acres of land on which she plans to grow wheatand corn. Each acre of wheat requires 4 hours of labor and $20 ofcapital, and each acre of corn requires 16 hours of labor and $40of capital. The farmer has at most 800 hours of labor and $2400 ofcapital available. If the profit from an acre of wheat is $80 andfrom an acre of corn is $100, how many acres of each crop shouldshe plant to maximize her profit?

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The problem is converted to canonical form by adding slacksurplus and artificial variables as appropiate1 As the constraint1 is of type we should add slack variableS12 As See Answer

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