Page 73 - Mathematics_Form_3

Linear programming

Steps for solving linear programming y
problems graphically
40
The following are the steps of graphing
linear programming problems:
FOR ONLINE READING ONLY
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1. Formulate the linear programming 3x+2y=80
problem. B(0, 24)
2. Replace an inequality symbol with 20
an equals sign to form an equation C(16, 16)
of the boundary line of the graph. 10 x=0 x+2y=48
3. Draw the straight line that serves Feasible region
as a boundary line. Use dotted lines
if an inequality sign < or > is used. A(0, 0) 10 y=0 20 D(26.7, 0) x
3 30
0
Use a solid line if an inequality sign
≤ or ≥ is used.
4. Identify the feasible region by testing
any convenient point (coordinates) Solution
which does not lie on the boundary. The shaded region ABCD represents the
Substitute the coordinates of the point feasible region. Hence, the maximum
in the inequality. If the inequality value of f occurs at the corner points
is satisfied at the tested point, then of the feasible region. The following
the point lies in the feasible region, table shows the corner points and the
otherwise it does not lie in the corresponding values of the objective
feasible region. function.
5. Identify the coordinates of the corner Corner Values of the objective
points of the feasible region.
Mathematics for Secondary Schools Example 3.4 feasible function ( ,f xy = = 4x + 3y
points
6. Evaluate the objective function at the
of the
corner points to obtain the optimal
)
value which may either be maximum
region
or minimum depending on the nature
f =
=
4(0) 3(0) 0+
A(0, 0)
of linear programming problem.
4(0) 3(24) 72+
f =
=
B(0, 24)
4(16) 3(16) 112+
f =
C(16, 16)
Determine the maximum value of
)
3y of the feasible region
f
( ,xy =
4x +
represented by the linear programming D(26.7, 0) f = 4(26.7) 3(0) 106.8+ =
problem shown in the following figure. Therefore, the maximum value of f is
112 and it is attained at point (16, 16).
66 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 66