Anyone please help solving this optimization problem.

Attachment 27979

maximize $\displaystyle 2x_1x_2+3x_2x_3+4x_1x_3$subject to $\displaystyle 5x_1+6x_2+7x_3 = 10$

It does not seem like I can proceed by using Lagrangian method. Could anyone please give me how to proceed ?

Thanks.