In this problem, well study the uncertainty underlying a professional hockey season viathe following entropy functionln piS(p1,..., p30)=30pii=1ln 2in terms of the probabilities pi that each of thirty teams will win the season. UseLagrange multipliers and direct substitution to determine the extreme values (maximumand minimum) of the entropy entropy function S(p1,..., p30) subject to the constraintsp1+...+ p30=1 and 1pi 0.Hints:use the Lagrange multiplier rule with the equality constraint p1+...+ p30=1 toidentify one candidate,use direct substitution from the endpoints of 1 pi 0 to identify 30 morecandidates, andcompare the entropy values of the 31 candidates to determine the maximum valueand minimum value (note that lHopitals Rule ensures you can evaluate 0ln(0)=0even though ln(0)=).