Module A 100 marks – 3 hours
Q.1 (a) Companies A and B earned profits of Rs. 600,000 and Rs. 1,320,000 respectively during
2009. It is estimated that future annual profit would increase @ 8% and 5% respectively. In
which year, the profit of both companies would be equal? (05 marks)
(b) Given that 0328 22 yxyx ; express ‘y’ in terms of ‘x’. (03 marks)
Q.2 Mr. Hamid plans to invest equal annual amounts in a bank for five years starting from January 1,
2011 in order to have the following amounts available with him:
Rs. 1.0 million for the marriage of his daughter on January 01, 2018.
Education expenses of his son consisting of four annual payments of Rs. 240,000
commencing from January 1, 2019.
If the bank agrees to pay interest @ 10% per annum compounded annually, calculate the amount of
annual deposits which he would be required to invest. (08 marks)
Q.3 (a) If 12
2
x
e
y
x
, show that x
e
xy
dx
dy
4
3)14(
(07 marks)
(b) Find out the coordinates of the relative maxima, minima and point of inflexion of the
following function:
932
3
123 xxxy (10 marks)
Q.4 Stable Limited manufactures two models of refrigerators. Deluxe Model requires 14 hours of
Department A and 40 hours of Department B. Standard Model requires 7 hours of Department A
and 30 hours of Department B. Each month, a maximum of 2100 hours are available in
Department A and 8400 hours in Department B. The company makes a profit of Rs 5,000 on each
Deluxe Model and Rs 4,000 on each Standard Model.
(a) Construct the set of constraints and the objective function for profit maximization.
(b) Draw the graph and identify the feasible region, clearly indicating its boundaries.
(c) How many refrigerators of each model should the company manufacture per day to
maximize its profit? (09 marks)
Q.5 (a) Express the following system of equations in matrix form and determine their solution, if
any, using matrix algebra.
2052
zyx
40723
zyx
3063
zyx
(04 marks)
(P.T.O.)
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