Page 106 - PM Integrated Workbook 2018-19

Chapter 4

3.4 Drawing graph and 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

 For Department B, if X =0, Y = 900 and if Y = 0, X = 2,250

 For Department C, if X =0, Y = 2,000 and if Y = 0, X = 1,000

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