The property manager of a city government issues chairs, desks, and other office furniture to city buildings from a centralized distribution center. Like most government agencies, it operates to minimize its costs of operations

In this distribution center, there are two types of standard office chairs, Model A and Model B. Model A is considerably heavier than Model B, and costs $20 per chair to transport to any city building; each model B costs $14 to transport. The distribution center has on hand 400 chairs—200 each of A and B.

The requirements for shipments to each of the city's buildings are as follows:
Building 1 needs at least 100 of A
Building 2 needs at least 150 of B.
Building 3 needs at least 100 chairs, but they can be of either type, mixed.
Building 4 needs 40 chairs, but at least as many B as A.

Formulate this problem as a linear program. (Hint: there are eight decision variables because we need to know how many of each chair (A and B) to deliver to each of the four buildings).

Let the variables be A1, A2, A3, and A4 for the type A chairs sent to each of the four buildings, and B1, B2, B3, and B4 for the type B chairs sent to each of the four buildings.

Minimize 20A1 + 20A2 + 20A3 + 20A4 + 14B1 + 14B2 + 14B3 + 14B4
Subject to
A1 + A2 + A3 + A4 ? 200
B1 + B2 + B3 + B4 ? 200
A1 ? 100
B2 ? 150
A3 + B3 ? 100
A4 + B4 ? 40
-A4 + B4 ? 0
all variables ? 0