Business Decision Modeling$-$Integer Programming

A man would like to open a truck dealership in Seattle. While he is setting up his

business, he needs to decide how to allocate his total available space of $700m^{{?}^{{?}^{?}}}2$ and a

construction budget of $220\mathrm{.}000$ $ among four departments: sales, service, spare parts,

and showroom. Every department will have a unit construction cost and a unit profit per

month per square meters allocated. Besides if he decides to include a department in his

dealer, there is a minimum space requirement to be allocated and also fixed cost of

construction. The related data is summarized below:

Develop an integer programming model to help the man to decide how much $($if any$)$

space should be allocated to each potential department to maximize the total profit such

that total construction budget, total space, and minimum space constraints will be

satisfied. Please clearly define:

Decision variables

Objective function

Constraints.