Multivariable calculus optimization problem I need to optimi

Multivariable calculus optimization problem

I need to optimize f(x,y) = 10a + 6b + 8c, where a = sqrt(x^2+y^2), b = sqrt((x-560.5)^2 + (y-1241.3)^2), c = sqrt((x-1939.3)^2 + (y-1388.4)^2)

I have found the partials of both, setting them equal to zero gives the following system of equations:

10x/a + (6x-3363)/b + (8x-15514)/c = 0

10y/a + (6y-7447)/b + (8y-11107)/c = 0

The algebra to accomplish this would be horrendous, is there an easier way?

I think this is the most simple way to solve these type of problems. other ways are more complex than this