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## Homework Statement

max Z = max (xεS) {min {Z

_{1}, Z

_{2}...Z

_{q}}}

where Zi=C

_{1}

^{i}x

_{1}+ C

_{2}

^{i}x

_{2}+...+C

_{n}

^{i}x

_{n}

## Homework Equations

Constraints need to be defined to set up the problem.

## The Attempt at a Solution

The first few Z equations would be:

Z

_{1}=C

_{1}

^{1}x

_{1}+ C

_{2}

^{1}x

_{2}+...+C

_{n}

^{1}x

_{n}

Z

_{2}=C

_{1}

^{2}x

_{1}+ C

_{2}

^{2}x

_{2}+...+C

_{n}

^{2}x

_{n}

Z

_{q}=C

_{1}

^{q}x

_{1}+ C

_{2}

^{q}x

_{2}+...+C

_{n}

^{q}x

_{n}

I think the best way to ensure that the Z is at a minimum is to define the inequalities below:

Z < Z

_{1}

Z < Z

_{2}

...

Z < Z

_{q}

This ensures that we pick the minimum value of Z. But these constraints should also include some way to maximize x and I am confused as to how to include that.