Considering a function Y=Y(L1,L2,a) how can I compute which configurations of L1,L2,a give the value Y=-0.81 and pick those of them that satisfy L1+L2+a=minimum?

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Tasos Charitonidis 2014-9-30

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https://ww2.mathworks.cn/matlabcentral/answers/156741-considering-a-function-y-y-l1-l2-a-how-can-i-compute-which-configurations-of-l1-l2-a-give-the-value

Hi all, I apologize in advance if this question is trivial! I would like to share the following: I have generated in maxima, after some matrices multiplications, an expression for Y:

Y=-((a^3*sin(a)^4*L1^2+(4*a^2-4*a^2*cos(a))*sin(a)^3*L1+
(4*a*cos(a)^2-8*a*cos(a)+4*a)*sin(a)^2)*L2-2*a^2*cos(a)*sin(a)^3*L1^2+
((6*a*cos(a)^2-8*a*cos(a))*sin(a)^2-2*a*sin(a)^4)*L1+(4*cos(a)-4)*sin(a)^3+
(-4*cos(a)^3+12*cos(a)^2-8*cos(a)-4)*sin(a)+4*a)/(a);

I would like to compute which configurations of L1,L2,a give the value e.g Y=-0.081, given that we fix the ranges for L1,L2 and a as follows:

 L_range=0.5:0.05:2.45; %L is length in meters
 alpha= 0.5:0.2:7; % a is bending angle in degrees. To convert in radians multiply with *pi/180
  
 for k1 = 1:length(L_range)
  for k2 = 1:length(alpha)  
        
    L1 = L_range(k1);
    L2 = L_range(k1);
    a  = alpha(k2);
 Y=-((a^3*sin(a)^4*L1^2+(4*a^2-4*a^2*cos(a))*sin(a)^3*L1+
(4*a*cos(a)^2-8*a*cos(a)+4*a)*sin(a)^2)*L2-2*a^2*cos(a)*sin(a)^3*L1^2+
((6*a*cos(a)^2-8*a*cos(a))*sin(a)^2-2*a*sin(a)^4)*L1+(4*cos(a)-4)*sin(a)^3+
(-4*cos(a)^3+12*cos(a)^2-8*cos(a)-4)*sin(a)+4*a)/(a);
 if Y=-0.081
 ...
  .. 
   . 
    
     end
    end

How can I then find which of the L1,L2,a configurations that give Y=-0.081 give the minimum sum L1+L2+R*a where R is e.g. R=1 meter ? Is there a built in function that I can take advantage of?

Thanks and regards!