st: Mata Optimize with Inequality Constraint

[Tsegaye Tenagne <tsgelectric@gmail.com>]

Dear All ,
I have the following exponential function that shows revenue per item
for an arcade floor. The coefficients are from regression results. I
have area and product type dummies, total number of similar units in
the floor, along with many other variables in the regression. Below is
a simplified form of my revenue equation.
Revenue= exp(constant:+Area_fe:+producttype_fe:+b_N:*unit:+b_N2:*(unit:^2)+b_N3:*(unit:^3)
+ b_New:*new:+b_New2:*(new:^2)+b_New3:*(new:^3))*(Optimal Units)
Units=number of similar items on floor
New = number of new items on floor (less than certain age)
I want to use mata  _optimize() function to arrive at the optimal
products combinations that can generate the floors maximum revenue.
 Below is a simplified matrix of variable that I am interested in
 Area       Product Type               Units           Optimal_Units
    Similar_Units  (unit)         Decision
A              X                                2                   2
                           10                             0
A              Y                               5                   5
                           9                              0
A              Z                               6                   6
                           6                              0
A              P                              3                   3
                           6                             0
B              X                               8                   8
                          10                             0
B              P                              2                   2
                           6                             0
C              P                              1                   1
                           6                             0
C             Q                               5                   5
                           5                             0
C             Y                               4                   4
                           9                             0

I wanted to use separate decision column for decision variable because
new units have different demand compared to existing units. Decision
(argument) is a column vector. The optimal units are defined as the
decision (add or remove) + current units. The decision variable can
only take integers (positive if additional items are required or
negative if item has to be removed from the floor). The number of
similar units is the count of similar items on the floor (example sum
of x's in A, B and C =10)

My question is:

 How do I tell mata that I have column vector evaluators?
Can I use stata inside mata to generate aggregate values?  example
stata("bysort product_type:egen similar_units=total(units)"
How do I add inequality and integer constraints? Is mata capable of
adding inequality and integer constraints?
How do I add collapsed matrix of constraints?  Example below ( the
total number of units in each area should be the same before and after
the change).

 Area      Product Type   Units        Optimal units
A              X                  2                  2
A              Y                 5                  5
A              Z                 6                  6
A              P                3                  3
B              X                 8                  8
B              P                2                  2
C              P                1                  1
C              Q                5                 5
C              Y                4                 4
=
 Area    units
A          16
B          10
C          10

My apology for the lengthy email.
Any help is very appreciated

Tsegaye
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