The described LP Problem is the following:
Problem Name: "LPDemo" identified by <PbId

Here is the code of the Visual basic subroutine that describes this LP problem:

' Defining the Problem Identifier as Long and Public
Public PbId As Long

Private Sub GenerateModel()
  ' Defining indices
  Dim i, j As Integer

  ' Defining the returned status of the functions as Long
  '(available for almost functions)
  Dim status As Long

  ' Opening the problem LPDemo
  PbId = ezmOpenPb("LPDemo")

  ' Define the optimization criterion as Maximize with
 ' returning the status
  status = ezmOptCri(PbId, EZM_MAX)

  ' Describe the linear terms X1 and X2 of the objective function
  status = ezmCCoef(PbId, "X1", EZM_SET, 2#)
  status = ezmCCoef(PbId, "X2", EZM_SET, 1#)

  ' Describe the linear terms Y of the objective function
  For j = 1 To 4
    status = ezmCCoef(PbId, "Y" & j, EZM_SET, 1#)
  Next j

  ' Describe the constraint
  ' The sense of the constraint "Equal ..."
  status = ezmConType(PbId, "Constraint", EZM_EQCON)

  ' The left-hand side (Yi, i=1,..., 4)
  For j = 1 To 4
    status = ezmACoef(PbId, "Y" & j, "Constraint", EZM_SET, 1#)
  Next j

  ' The left-hand side (X1)
  status = ezmACoef(PbId, "X1", "Constraint", EZM_SET, 4#)

  ' The left-hand side (X2)
  status = ezmACoef(PbId, "X2", "Constraint", EZM_SET, 1#)

  ' The right-hand side
  status = ezmBCoef(PbId, "Constraint", EZM_SET, 2#)

  ' Specify the type of the variables Y(j), X1 and X2
  ' as "continuous variables"
  For j = 1 To 4
    status = ezmVarType(PbId, "Y" & j, EZM_CONVAR)
  Next j
  status = ezmVarType(PbId, "X1", EZM_CONVAR)
  status = ezmVarType(PbId, "X2", EZM_CONVAR)

  ' Specify the non-negativity of the variables Yi, X1 and X2
  For j = 1 To 4
    status = ezmLwCoef(PbId, "Y" & j, EZM_SET, 0#)
  Next j
  status = ezmLwCoef(PbId, "X1", EZM_SET, 0#)
  status = ezmLwCoef(PbId, "X2", EZM_SET, 0#)

  ' Specify The upper bounds of the variables Yi, X1 and X2
  For j = 1 To 4
    status = ezmUpCoef(PbId, "Y" & j, EZM_SET, 1#)
  Next j
  status = ezmUpCoef(PbId, "X1", EZM_SET, 2#)
  status = ezmUpCoef(PbId, "X2", EZM_SET, 2#)

End Sub

' Here is the subroutine to solve the described LP problem
' It uses the same problem identifier (PbId) defined as Public

Private Sub Solve()
  ' Defining the returned status of the functions as Long
  Dim status As Long

  ' Solve the problem LPDemo using EZMMSE-SMALL-Version Solver
  status = ezmSolve(PbId, EZM_LP, EZM_MSE_SMALL)

End Sub

' Here is the subroutine to get the solution of the LP problem
' It uses the same problem identifier (PbId) defined as Public

Private Sub Results()
  ' Defining the returned status of the functions as Long
  Dim status As Long

  ' Add two text box components named Text1 and Text2 to your Form
  ' and run the code to get the Objective Value and the X1 value
  Text1.Text = CStr(ezmGetZ(PbId))
  Text2.Text = CStr(ezmGetX(PbId, "X1"))

  ' Get the solution with all the parameters and variables
  ' and open the "PbSolution.txt" (in C:\) using a text viewer
  status = ezmWritePb(PbId, "C:\PbSolution.txt")

End Sub