2.2 Drawing the graph and identifying the feasible region Drawing the graph
§ 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.
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Step 4 of the linear programming model is to represent the constraints as straight lines on a graph. We do this below. In the meantime, this section contains basic revision for students who are not familiar with the process of graphing a straight line.
To begin with, we must have a linear relationship between two measurements.
Examples y = 3x + 1
y = 2x + 42 etc.
Note:
1 To recognise a linear relationship the equation must have only ‘x’ not ‘x’ to the power of anything, e.g. x2.
2 A straight line has two characteristics:
(i) a slope or gradient – which measures the ‘steepness’ of the line
(ii) a point at which it cuts the y axis – this is called the intercept:
y = (slope × x) + intercept
e.g. y = 2x + 3
∴ the gradient is 2 and the point at which the line cuts the y axis is 3.
3.
To draw a straight line graph we only need to know two points that can then be joined.
Consider the following two equations:
(i) y = 2x + 3
(ii) y = 2x – 2 |
发表于 2012-2-23 17:09:42
