Walzer Corporation manufactures two types of widgets A and B. It has two factories F1 and F2 each one capable of producing
the two types of widgets. F1 can produce up to a total of 150 units. F2 can produce up to a total of 100 units.

Each factory can produce any combination of amounts for A and B without incurring additional costs. For example F1 can
produce 150 units of A and none of B or 50 units of A and 100 units of B. Similarly F2 can produce 50 units each of A and B or 30 units of A and 70 units of
B.

Walzer has two customers C1 and C2. Customer C1 needs 100 units of A and 50 units of B. Customer C2 needs 50 units of A and
50 units of B.

The unit production costs (including shipping) the available supplies and customer demands are shown in the table
below.

a. Formulate algebraically this variant of the
transportation problem by defining the decision variables the objective function and the constraints. The objective is to minimize the total production
(including shipping) costs while satisfying the demands of each customer for each product type.

b. Formulate the problem in Excel. Use Solver to find
the optimal amounts of products A and B that each factory has to produce (and ship) to each customer such that the total production (including shipping) cost
is minimized.

[Hint: Introduce additional decision variables. With this you will be able to account for all possible ways to breakf 150
and 100 units respectively for F1 and F2].