ables
         </p>
         <p><img src="manual_eq80000.png" alt="$$ \min x_1x_4(x_1 + x_2 +x_3) + x_3$$"></p>
         <p>subject to</p>
         <p><img src="manual_eq05068.png" alt="$$x_1x_2x_3x_4 - x_5 - 25 = 0$$"></p>
         <p><img src="manual_eq72171.png" alt="$$x_1^2+x_2^2+x_3^2+x_4^2-x_6-40 = 0$$"></p>
         <p><img src="manual_eq97674.png" alt="$$1\leq x_i\leq 5,\ i=1,2,3,4,\quad x_i\geq 0,\ i=5,6$$"></p>
         <p><img src="manual_eq95348.png" alt="$\pmatrix{x_1&amp; x_2&amp; 0&amp;0\cr x