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A quadratic programming model is an optimization model with n decision variables and m linear constraints, and of the form:

Minimize Z=12xTQx+cTx  

Subject to: Axb  

x0  

Where x is the n by 1 column vector of decision variables and xT is its transpose, Q is an n by n symmetric matrix of the objective parameters, c is an n by 1 vector of additional objective parameters, A is an m by n matrix of constraints parameters, and b is an m by 1 vector of constraints’ right hand sides.

1. Explain how quadratic programming is used in the real world. Provide a specific example from your own line of work, or a line of work that you find particularly interesting. Indicate explicitly and qualitatively what Z, x, Q, C, A, and b are in your example.
2. Describe how you would handle solving a quadratic programming problem in which some of the problem parameters are random variables as opposed to being constant values. Make sure that you include a specific example of application in your response.