Integer Programming My brother would like to open a truck dealership in Konya. While he is setting up his business, he needs to decide how to allocate his total available space of $700$ m$2$ and construction budget of $220000$ TL among four departments: sales, service, spare parts, and showroom.

Every department will have a unit construction cost and 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.

Department Construction Unit cost of

Fixed cost of Construction

per m$2$ Profit per m$2$ Minimum space needed

Sales $1200020030110$

Service $2000030010100$

Spare Parts $150001502580$

Showroom $3100035040200$

Develop an integer programming model to help my brother 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, and

$*$constraints$.$