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21. (a) C   0.4x  x  8x  200,R   200x  x  2 ,   192x  x  2.4x  200
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(b) The output level is 40 units and the price is RM120 when the profit is maximized

22. = 5, = 100; 50

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23. (a) = −21, = 5; y  10x  21x  12x  5
1 2459
(b) y   x 
12 300

24. = 2, = −1; = − + 1

25. = −3

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26. (a) ' R   x   0.2x  40,    x   0.4x  60x  3000
(b) The average revenue is RM 42 and the loss is RM 1960 when the cost is minimized

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27. (a) R   x   0.02x  40;    x   0.02x  50x  20000
(b) The production level of 1250 will maximize the profit. The maximum profit is
RM 11 250.

(c) The price per unit is RM 75

28. = 19 − 23

, 
29. (a) Stationary points: 1,  7   2, 10  
 

 6   3 


(b) Minimum point is 1, 7   and maximum point is  2, 10  


 6   3 
30. (a) C '   300, 'q  R   400 2 ,q   q D   400q   q
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
(b)    100q  q q  500; 50 units per week shall be produced
(c) Total revenue is RM 17500, profit is RM2000 and selling price per unit is RM350