(a) Evaluate the following integrals

[2 Marks]

ii.

[3 Marks]

12

00

[3 Marks]

(b) The market research department of a chain of pet stores test marketed their aquarium pumps in several of their stores in a test city. They found that the weekly demand of aquarium pumps is given approximately by: p=12-2lnx

0

where x is the number of pumps sold each week and p is the price of one pump. If each pump costs the chain $ 3, how should it be priced in order to maximize the weekly profit? Marks]

[4

J

O

(c) A company produces three products P, Q and R using raw materials A. B and C. One unit of P requires 1, 2 and 3 units of A, B and C respectively. One unit of Q requires 2, 3 and 2 units of A, B and C respectively. One unit of R requires 1, 2 and 2 units of A, B and C respectively. The number of units available for raw material A, B and C are 8, 14 and 13 units respectively. Using the matrix method, utilize resources.

determine the number of units of each product to produce in order to

completely

the

available

[8 Marks]