Just wonder if anyone knows how I can improve on minimizing this large poly, subject to constraints: Download The minimum found was 82.7 It has found a local minima, but there must be a global minima. Do i really have to splash out on the GOT package?

Wonder is someone can help I need to Minimize the non-linear objective function: Obj:=(1/4*a[1]+3/4*a[2]+7/8*a[3]+15/8*a[5]+2*a[6]+19/8*a[7]+21/8*a[8]+1/4*b[1]+ 3/4*b[2]+7/8*b[3]+15/8*b[5]+2*b[6]+19/8*b[7]+21/8*b[8])^2 subject to the following constraints: CON1:=add(a[n],n=1..8)=4 CON2:=add(b[n],n=1..8)=4 CON3:=seq(a[n]+b[n]=1,n=1..8) CON4:=seq(or(a[n]=0,b[n]=1),n=1..8) With(Optimization): NLPSolve(Obj,{CON1,CON2,CON3,CON4},assume = nonnegative); produces this: Error, (in Optimization:-NLPSolve) constraints must be specified as a set or list of equalities and inequalities

Does anyone know how to work out the largest triangle that can be enclosed within an ellipse (both in 2D)? For any triangle, Area:=sqrt(s*(s-a)*(s-b)*(s-c)) where s:=(a+b+c)/2 and a,b,c are the length of the sides. Say the ellipse is equation 1/9*x^2+1/4*y^2 = 1 hence y: = -2/3*(-x^2+9)^(1/2) or +2/3*(-x^2+9)^(1/2) Given three points (x1,y1), (x2,y2), (x3,y3) Eg distance from (-x1,-y) to (-x2,y) with(student): a:=distance([-x1, subs(x=-x1,-2/3*(-x^2+9)^(1/2) )], [-x2, subs(x=-x2, +2/3*(-x^2+9)^(1/2))]); (note the sign of y) and so forth for b and c. there has to be a more eloquent (calculus) way.

Hi I wonder if anyone can assist with the Maple commmand to do total derivatives. For example, tan(theta)=1/x I want to know if there is a direct command to differentiate this equation w.r.t t (time). From memory, if I input D(tan(theta)=1/x), Maple outputs: tan(theta)D(theta)=-1/x^2 Dx the correct result should be: sec^2(theta)d(theta)/dt = -1/x^2 dx/dt thanks in advance Brian