Page 97 - Microsoft Word - 00 Prelims.docx

Planning with limiting factors

3.4 Drawing graph Identifying the feasible region

 Step 4 of the linear programming model is to represent the constraints as
straight lines on a graph.

 In order to plot the constraints it is normally best to compute the intercepts of
the equalities on the horizontal and vertical axes.

 Thus, x and y are each set equal to zero in turn and the value of y and x
computed in these circumstances All the constraints are straight lines so each
can be drawn by joining two points. In linear programming questions, it is often
easiest to get the two end points – i.e. where the lines cross the x and y axes.

 For each constraint line, we then need to consider whether the acceptable
(feasible) co-ordinates are below or above the line. All of the constraints here
are " ≤ " types, so acceptable solutions are to the left/below the lines giving the
feasible region ABCDE.

Example 2, continued

To draw Constraint 1 (constraint in Department A), we take the inequality '8x +
10y ≤ 11,000 hours' and turn it into an equation: 8x + 10y = 11,000. To draw
this constraint, we need two points.

If X = 0, Y = 11,000 ÷ 10 so Y = 1,100

 Likewise, if Y = 0, X = 11,000 ÷ 8 so X = 1,375

 If X =0, Y = 900 and

 If Y = 0, X = 2,250

91