Page 79 - Mathematics_Form_3

Linear programming

Subject to: 5x + ≥ 10
y
2x + 2y ≥ 12
x + 4y ≥ 12

x ≥ 0, y ≥ 0
FOR ONLINE READING ONLY
The graph of the constraints is shown in the following figure.

y

A(0, 10)
10

8
Feasible region
6
B(1, 5)
4

C(4, 2)
2
x=0 y=0 x+4y=12 D(12, 0)

-2 0 2 4 6 8 10 12 14 x

-2 5x + y = 10 2x + 2y=12

The corner points and the values of the objective function are shown in the

following table. Values of the objective function
Mathematics for Secondary Schools A(0, 10) f = 3000(0) + 2000(10) = 20000
Corner points of the
feasible region
f (x, y) = 3000x + 2000y

f = 3000(1) + 2000(5) = 13000
B(1, 5)
f = 3000(4) + 2000(2) = 16000
C(4, 2)
D(12, 0)
f = 3000(12) + 2000(0) = 36000
The minimum value of the objective function is at point B(1, 5) which is Tshs
13,000.

Therefore, in order to minimize the cost while meeting the requirements, John
should purchase 1 litre of liquid product and 5 cartons of powder product.

72 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 72