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11. (a) C   50x  x  35

70
(b) p   x   0.001x  100
x
(c) Maximum profit is RM 625035

12. (a) The company will loss RM 40000 from a production of 100 barrels

(b) 10 units will maximize the profit. The maximum profit is RM 500

1
13. a  ,b  4
2

2
2
2
14. (a) C   5x  x  40 ;R   240x  x  20 ;   200x  x  25x
x
x
(b) The quantity is 6 units and the price is RM 120 when the total revenue is maximized
(c) The profit is RM 400 and the total revenue is RM640.


dy y x
15.  ; The points are (2,2) and (−2, −2)

dx 2y x
16. (a) The price is 160
(b) The maximum revenue is RM 90 000

3 1
17. y  x 
2 2

18. (a) (0,0) is the minimum point and (4,64) is the maximum point
(b) Equation of tangent: y  24x  16

19. y  2x  3

20. (a) stationary points are (0,0), (-1,-3) and (1,-3); Maximum point: (0,-2), Minimum

point: (1,-3) and (-1,-3)
(b) y  24x  42