$3.$There are $4$ stores, each with $2$ inputs and $1$ output as given in table below. The inputs areThere are $6$ DMUs with a single input and single output case.

Assume this is an output$-$oriented VRS problem.

$(1)$Plot the VRS DEA frontier in the figure.

$(2)$ Point out the fully efficient DMUs.

$(3)$ Point out the inefficient DMU.

$(4)$ Point out the weakly efficient DMU.

the number of workers and the costs of the goods. The output is the profits.

$(1)$Formulate the input$-$oriented VRS envelopment model for DMU A$.$

$(2)$Formulate the input$-$oriented CRS multiplier model for DMU B$.$

$(3)$Formulate the output$-$oriented CRS envelopment model for DMU C$.$

$(4)$Formulate the output$-$oriented VRS multiplier model for DMU D$.$