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**1:** The following statements are true except for ...

**2:** What method would you use to maximize the function:

subject to the constraints:

x-x

x

where all variables are non-negative?

**3:** What is the starting point for the Karmarkar's projective
algorithm in `n`

dimensions?

**x**_{0} = **0**

,
where **0**

is the vector of zeros **x**_{0} = **1**/n

,
where **1**

is the vector of units**x**_{0} =
**e**_{n}/n

, where **e**_{n}

is
the unit vector for the component `x`_{n}

**x**_{0} =
**e**_{1}

, where **e**_{1}

is the unit vector
for the component `x`_{1}

**4:** Identify entering and departing variables for the next
iteration of the dual simplex method.

`x` |
`x` |
`x` |
`x` |
`x` |
||

`x` |
0 | -8 | -5 | 1 | 0 | -3 |

`x` |
1 | -1 | 2 | 0 | 0 | 1 |

`x` |
0 | -3 | -4 | 0 | 1 | -1 |

`z` |
0 | -4 | -5 | 0 | 0 | 3 |

`x`_{4}

is
departing variable, `x`_{2}

is entering variable `x`_{4}

is
departing variable, `x`_{3}

is entering variable `x`_{5}

is
departing variable, `x`_{2}

is entering variable `x`_{5}

is
departing variable, `x`_{3}

is entering variable
**5:** Suppose you have found an optimal solution with
the value `z = z`

in the problem of
minimization of _{0}` z = `

, subject to the constraints
**c x**

If a new variable `x' >= 0`

is added to
the problem, what may happen to the optimal objective function
value `z`

?
_{0}

`z`_{0}

is not affected by the new variable
`x'`

`z`_{0}

may increase `z`_{0}

may decrease `x'`

may have empty
feasible region

Your Results: