Consider a set of products, with their profit $[$$$/$unit$]$ and resource requirements: e$.$g$.,[$hours$/$unit$].$ In the example shown below, we have $6$ products and $5$ resources.

We want to find an optimized production plan that satisfies all stated resource usage limits and maximizes the total profit.

For simplicity, we can assume that all products can be produced in arbitrary continuous amounts. This is acceptable for large production volumes, leading to LP models.

$\backslash$table$[[$Model Input Data,,,,,,,,,$],[,,,,,,,$Constraints,$],[$Resources Used Per Product Unit,,,,Resources,Relations,Resources$],[$Product $1,$Product $2,$Product $3,$Product $4,$Product $5,$Product $6,$Required,,Available$],[$Resource $1,1,2,3,2,3,4,,,4000],[$Resource $2,2,2,4,3,3,4,,,2500],[$Resource $3,2,3,2,3,1,3,,,3200],[$Resource $4,1,3,4,1,2,3,,,1800],[$Resource $5,2,3,3,2,2,5,,,2400],[$Unit Profit $[$$$],15,20,25,22,18,30,,,]]$

Decision Variables

Units Produced

Units Min

Units Max

$\backslash$table$[[,,,,,],[20,20,20,20,20,20],[250,250,250,250,250,250]]$

Objective Function

Total Profit $[$$$]$