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Statistics - Simplex method

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Study problem: 4-10

Solve the following linear programming model by the simplex method.

Maximize Z= $40x1 + $30x2

Subject to: 2 x1 + 2 x2  240

2 x1  120

2 x2  80

x1, x2  0

Study Problem: 4-12

Solve the following linear programming model by the simplex method.

Minimize Z = $2 x1 + $3 x2

Subject to: 2 x1 + 5 x2  30

4 x1 + 2 x2  28

x1, x2,  0

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Statistics: Dreskin Development Co construction of two apartment complexes.

See attached file for clarity.

The Dreskin Development Company is building two apartment complexes. It must decide how many units to construct in each complex subject to labor and material constraints. The profit generated for each apartment in the first complex is estimated at $900, for each apartment in the second complex, $1,500. A partial initial simplex tableau for Dreskin is given in the following table:

Cj $900 $1500 $0 $0

Solution Mix X1 X2 S1 S2 Quantity
14 4 1 0 3360
10 12 0 1 9600


(a) Complete the initial tableau.
(b) Reconstruct the problem's original constraints (excluding slack variables).
(c) Write the problem's original objective function.
(d) What is the basis for the initial solution?
(e) Which variable should enter the solution at the next iteration?
(f) Which variable will leave the solution at the next iteration?
(g) How many units of the variable entering the solution next will be in the basis in the second tableau?
(h) How much will profit increase in the next solution?

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