Optimal Point in Integer Programming

Conceptual Overview: Explore how the optimal point is chosen from the feasible set in integer programming.

Eastborne Realty has $$2$ million to invest in apartment buildings $($A$)$ and townhouses $($T$).$ A prior applet established the feasible region in the graph below. The highlighted region represents feasible combinations of the number of apartment buildings and townhouses the company might purchase given the company's investment constraints. Additionally, only whole apartment buildings and townhouses may be purchased, so possible investments are limited to the dots within the feasible region. The dotted red line indicates the extreme dots, which are the potential optimal choices. The company expects the annual cash flow, after deducting expenses, to be $$10$ thousand for townhouses and $$15$ thousands for apartment buildings, yielding a total of $10$ T $+15$ A$.$ This equation is represented by the diagonal line in the graph. Drag the line until it gives the maximum value while simultaneously going through one of the feasible points. Note: Due to the resolution of the screen, it is difficult to place the line exactly on the best point in the feasible region. Once you are close, double click on the graph and the line will move to the optimal position.

$282$ T $+400$ A $<=2,000$ Funds available $($$$1,000$s$)$

$4$ T $+40$ A $<=140$ Manager's time $($hours$)$

T $<=55$ Townhouses available