Part III.

$($Full Score: $40$ Points$)$

There are $5$ factories, each with $2$ inputs and $2$ outputs as given in table below.

$\backslash$table$[[$DMU$,$Input$1,$Input$2,$Output$1,$Output$2],[$A$,50,55,130,80],[$B$,100,45,190,90],[$C$,150,65,280,30],[$D$,200,95,420,70]]$

$$ MBA $46$ System Performance Evaluation Method

Page $4$ of $6$

$(1)$Formulate the output$-$oriented VRS multiplier model for DMU A$.$

$(2)$Formulate the output$-$oriented CRS envelopment model for DMU B$.$

$(3)$Formulate the input$-$oriented VRS envelopment model for DMU C$.$

$(4)$Formulate the input$-$oriented CRS multiplier model for DMU D$.$