Answer Happy

Can you model the following question, both algebraically (i.e.,
in terms of formulas, sums, etc.) and in expanded-detailed format
(i.e., state each constraint and objective with respect to data in
details)?
John Galt Shipping wishes to ship a product that can be made at
two different factories to three different warehouses. They can
produce 48 units at Factory A if they spend $50 to build the
factory A, or produce 24 units at a factory building cost of $40.
Similarly, they can build Factory B with a capacity of 22 at a cost
of $45, or a capacity of 40 with a cost of $60. . They need 10
units in warehouse #1, 20 units in warehouse #2, and 10 units in
warehouse #3. Per unit transportation costs are shown in the table
below. At most two factories should be built. If one of
the factory is built at the lower capacity, the other one must be
built at higher capacity. How many units should be shipped from
each factory to each warehouse?
Warehouse #1
Warehouse #2
Warehouse #3
Plant A
$4
$2
$3
Plant B
$3
$2
$1