I have to maximize the following function -

Max A ${C}_{1}^{-m}/-m$ + (1-A) ${C}_{2}^{-m}/-m$

Subject to,

${C}_{1}$ ≤ 5(1-x) + x

${C}_{2}$ ≤ 3(1-x) + 7x

1≤x≤10

I wrote it as: L(x) = f(x) - ${\lambda}_{1}$(${C}_{1}$ - 5(1-x) + x) - ${\lambda}_{2}$(${C}_{2}$ - 3(1-x) + 7x) - ${\lambda}_{3}$(x-1) - ${\lambda}_{4}$(x-10)

Can I write last constraint as partioned into ${\lambda}_{3}$ and ${\lambda}_{4}$. Is there some other way to introduce such box constraints into the same problem?

Max A ${C}_{1}^{-m}/-m$ + (1-A) ${C}_{2}^{-m}/-m$

Subject to,

${C}_{1}$ ≤ 5(1-x) + x

${C}_{2}$ ≤ 3(1-x) + 7x

1≤x≤10

I wrote it as: L(x) = f(x) - ${\lambda}_{1}$(${C}_{1}$ - 5(1-x) + x) - ${\lambda}_{2}$(${C}_{2}$ - 3(1-x) + 7x) - ${\lambda}_{3}$(x-1) - ${\lambda}_{4}$(x-10)

Can I write last constraint as partioned into ${\lambda}_{3}$ and ${\lambda}_{4}$. Is there some other way to introduce such box constraints into the same problem?