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Answers

)
Chapter Three 7. Min f ( ,xy = 2y ≥ 400x + 150y
10
Subject to: x +

Exercise 3.1
FOR ONLINE READING ONLY
)
1. Max f ( ,xy = 2000x + 2500y
8. Min f ( ,xy ) 8000x= + 7500y
Subject to:x + 2y ≤ 6 Subjecto 2 t: x + 3y ≥ 6
3x + 2y ≤ 10 3x + 4y ≥ 8

x ≥ 0, y ≥ 0
x ≥ 0, y ≥ 0
2. Max f ( ,xy ) 3250x= + 3165y
9. Max f ( ,xy ) 10000x= + 13000y
Subject to: 4x + 3y ≤ 140 Subjec tt o: x + 2y ≤ 45
2xy+ ≤ 100 2x + 5y ≤ 80
x ≥ 0, y ≥ 0 4x + ≤ 60
y
)
3. Max f ( ,xy = 4450x + 3570y x ≥ 0, y ≥ 0
y
Subject to: 2x + ≤ 20 10. Max f ( ,xy = + y
)
x
x + ≤ 12 Subject to: x + 5y ≤ 2500
y
2x + 3y ≤ 15 −+ 2y ≤ 0
x
x ≥ , 0 y ≥ 0
x ≥ 0, y ≥ 0
)
4. Max f ( ,xy = 2330x + 1890y Exercise 3.2
Subjecto 2 t: x + 3y ≤ 30
x + ≤ 12 7000y 1. (a) Max f ( ,xy ) 11.2; (1.8,0.8)=
y
( ,xy
) 17; (4,3)=
Mathematics for Secondary Schools Subject to: 5x + 2y ≤ 4000 ( ,xy ) 6; (6,0)= (c) Min f , ( ,xy ) 3; (0,1)=    2 8  33  , 
0, y ≥
0
x ≥
(b) Min f
+
( ,xy
5. Max f
) 5000x=
y
2x + ≤
) 6; (6,0) or=
(d) Min f
( ,xy
4000
x +
2 8 

6y ≤
13500
Min f
or


0
0, y ≥
x ≥
33 

)
2500x +
6. Min f
( ,xy =
) 39.14;=
( ,xy
2y ≥
Subject to: x +
(f) Min f
x + ≥ 6 10 2850y (e) Max f ( ,xy ) 25; (5,10)=    10 26  7 , 7  
y
y
3x + ≥ 8 (g) Max f ( ,xy ) 150; (0,30)=
x ≥ 0, y ≥ 0 (h) Min f ( ,xy ) 24; (4,2)=
192 Student\s Book Form Three
18/09/2025 10:00:14
MATHEMATIC F3 SB.indd 192 18/09/2025 10:00:14
MATHEMATIC F3 SB.indd 192