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7. The average cost function and the demand function in RM for a furniture company is given

40
by   x   20 and   100 2p x   x . The company produces x units of table daily.
C
x
(a) Find the cost function.

(b) Find the revenue function

(c) The level of production to achieve the maximum profit
(d) Find the maximum profit


2
2
8. Find the equation of the normal to the curve 2x  2y  4xy  3 0 at the point (1, −4).

9. A firm has determined that the price function from the sale of q units of product is
p  30 0.5q . Find

(a) the marginal revenue when the price is RM 20,

(b) the quantity that should be sold to maximize its revenue,
(c) the selling price to ensure maximum revenue.

10. Find the equation of a tangent line at a curve 4xy  2 3x  5y when = 1.

11. Given the profit function and the average cost function (in RM), of a mechanical pencil are

35
2
   x   0.001x  50x  35 and   50C x   respectively. Determine
x
(a) the cost function,

(b) the demand function,

(c) the maximum profit

12. An oil well has a maximum daily production of 100 barrels. The owner estimate that the

daily profit    x (in RM) from a production of x barrels is

   100x  x  5 ,0   100.
x
x
2
(a) Determine whether profit or loss will be incurred from a production 0f 100 barrels