Question: minimization problem

UncertaityofCalibrat.mw

within the attached document, is the idea that I would like to develop with the optimization package.

I have the following set of data with their uncertainties:

Vector Measurements

<t1,t2,t3,t4,t5,R1,R2,R3,R4,R5>

<0.0000, 14.9980, 19.9990, 24.9980, 0.0000, 99.96650, 105.80750, 107.74890, 109.68870, 99.96650>

Vector of uncertainty:<0.0050, 0.0050, 0.0050, 0.0050, 0.0050, 0.0049 ,0.0049, 0.0048, 0.0050 ,0.0049>

The measured values of the temperatures t1,…, t5 are assumed to have
correlation coefficients r(ti, tj)=0.9, i≠j, and the measured values of the resistances R1,…, R5 are
assumed to have correlation coefficients r(Ri, Rj)=0.9, i≠j.

Gven the measured values z, the least squares estimates ζ and β of the quantities ζ and β are
found by minimizing the quadratic form

χ2(ζ;z) =(z−ζ)S⁻¹(z−ζ)

with respect to ζ =(t1..t5 , R1..R5 ) ^T under the five constraints 

R0 (1 + A*ti +B*ti²)-Ri,  i=1..5

I tried to do using LSSolve from optimization package.Could give me some suggestion. I developed
through a procedure, but neither is very efficient. As I like to do with LSSolve.