Solve using linear programming

NPCC offshore construction company needs to efficiently allocate welding tasks between two types of activities: pipeline welding and structural welding. Each activity has different profit margins and requires a different amount of welding hours and skilled welders. The company aims to maximize its profit while not exceeding the available welding hours and welders for a certain period. The company makes a profit of $$300$ for every hour of pipeline welding and $$250$ for every hour of structural welding. Total available welding hours are $1000$ hours, Total available skilled welders are $25$ welders, each hour of pipeline welding requires $2$ welders, each hour of structural welding requires $1$ welder.

Solve using linear programming

NPCC offshore company has a project of scaffolding for assembly and dis$-$assembly, and requires at least $80$ hours of Assembly and at least $70$ hours of Disassembly work.

Each hour of Assembly work requires $2$ laborers and $3$ units of materials, while each hour of Disassembly work requires $1$ labour and $2$ units of materials.

Due to budget and space constraints on the offshore platform, a maximum of $180$ units of materials can be used.

The cost of an hour of Assembly work &s $$150,$ and the cost of an hour of Disassembly work is $$100.$