I'm trying to solve the kind of linear equation below such that the sum of the unknowns is maximised, but have been unable to find the solution.

$\frac{10}{{y}_{1}}+\frac{12}{{y}_{2}}+\frac{15}{{y}_{3}}=50$

It may just be I am searching using the wrong terminology, if so direction of where to look would be greatly appreciated too.EDIT: To add some more information, the initial problem involved four equations.

${y}_{1}={K}_{1}/{x}_{1}$

${y}_{2}={K}_{2}/{x}_{2}$

${y}_{3}={K}_{3}/{x}_{3}$

${x}_{1}+{x}_{2}+{x}_{3}=X$

Where K and X values are given constants, and x and y values are unknown. I am trying to find a solution that maximises the sum of the y values.

It is from this problem that I simplified it to

$\frac{{K}_{1}}{{y}_{1}}+\frac{{K}_{2}}{{y}_{2}}+\frac{{K}_{3}}{{y}_{3}}=X$

With the first equation in the initial question just being arbitrary values.

$\frac{10}{{y}_{1}}+\frac{12}{{y}_{2}}+\frac{15}{{y}_{3}}=50$

It may just be I am searching using the wrong terminology, if so direction of where to look would be greatly appreciated too.EDIT: To add some more information, the initial problem involved four equations.

${y}_{1}={K}_{1}/{x}_{1}$

${y}_{2}={K}_{2}/{x}_{2}$

${y}_{3}={K}_{3}/{x}_{3}$

${x}_{1}+{x}_{2}+{x}_{3}=X$

Where K and X values are given constants, and x and y values are unknown. I am trying to find a solution that maximises the sum of the y values.

It is from this problem that I simplified it to

$\frac{{K}_{1}}{{y}_{1}}+\frac{{K}_{2}}{{y}_{2}}+\frac{{K}_{3}}{{y}_{3}}=X$

With the first equation in the initial question just being arbitrary values.