Page 84 - Past Year

82 | P a g e

C
26. The demand function p and the average cost function   x for a product are given as

3000
p  0.1x  40 and   0.5C x  x  20 , where x is the number of units of the product.
x
(a) Find the marginal revenue function and the profit function

(b) Find the average revenue and the profit or loss when the cost is minimized.

27. An electronic company produces calculators for the local market. The company finds that



the cost function is   50C x  x  20000 and the demand function is   100 0.02 ,
x
p
x
where represents the number of calculators and ( ) represents the price per calculator
in RM.
(a) Find the revenue function and the profit function

(b) Calculate the level of production that will maximize the profit. Hence, find the
maximum profit.

(c) Determine the price per unit when the profit is maximum.

2
3
x
28. Find the equation of tangent to the curve y  x  2x   1 at = 1.

1 1
3
2
f
29. Given   x  x  x  2x
3 2
(a) Find all the stationary points
(b) Determine the local maximum and minimum points

30. A manager of a washing machine manufacturer finds that the total cost function C(q) (in

RM) and the total revenue function R(q) (in RM), of producing and selling q units of



2
q
washing machine per week is given as C   300q  q  500 and   400q q
R
respectively. Find the
(a) marginal cost, marginal revenue and demand function
(b) profit function and number of units per week that should be produced in order to

maximize the profit.
(c) revenue, profit and selling price per unit at maximum profit.