Question

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Q#1: (i) Mr. Babar invests Rs. 150000 in a scheme for 8 years @ 6.5% compounded semiannually. Find how much he gain at the end of 8 years. (3)
(ii) (a) Draw the graph of (2)
() = {
1 > 0
0 = 0
−1 < 0
(b) Given the current interest rate of 6 percent compounded annually, find the present value of
$10,000 to be paid in (a) 1 year, (b) 3 years, (c) 5 years, and (d) 10 years. (5)
Q#2: (i) Find the level of income Y and the rate of interest i that simultaneously bring equilibrium
to the economy and estimate the level of consumption C, investment I, the speculative demand for
money , and the transaction-precautionary demand for money
, when (5)
(a) the money supply = 1000, C = 950 + 0.75Y, I = 310 − 125i,
= 264 − 175, and = 0.15, and
(b) = 800, = 1200 + 0.6, = 227 − 180, = 127 − 180, and =
0.2.
(ii) Use graphs to solve the linear programming problems. Minimize (5)
= 121 + 202
subject to
41 + 52 ≥ 100
421 + 152 ≥ 360
21 + 102 ≥ 80
1, 2 ≥ 0.
Q#3: (i) Solve problem by first finding the dual and then using the simplex algorithm. Minimize
(6)
= 2251 + 1802
subject to
81 + 2 ≥ 32
71 + 42 ≥ 112
1 + 62 ≥ 54
1, 2 ≥ 0.
(ii) Find the critical points at which each of the following average cost functions is minimized.
Check the second-order conditions on your own. (4)
(a) = 32 − 18 + 585
(b) = 2.252 − 27 + 768
Q#4: (i) What is the projected level of revenue in 3 years for a company with current revenues of
$48.25 million if estimated growth under continuous compounding is 8.6 percent? (4)
(ii) For each set of the following total revenue and total cost functions, first express profit π as
a function of output x and then determine the maximum level of profit by finding the vertex of
the parabola (6)
(a) = −6
2 + 1200, = 180 + 3350
() = −4
2 + 900, = 140 + 6100
Q#5(i) A car worth $6000 depreciates over the years at the rate ′() = 250( − 6) for 0 ≤ t ≤
6. Find the total amount by which the car depreciates in (a) the first 3 years and (b) the last three
years. (2)
(ii) A company decides to set up a small production plant for manufacturing electronic clocks. The
total cost for initial set-up (fixed cost) is . 9 ℎ. The additional cost (i.e., variable cost) for
producing each clock is . 400. Each clock is sold at . 1000. During the first month,
1500 clocks are produced and sold: (8)
(a) Determine the cost function () for the total cost of producing clocks.
(b) Determine the revenue function () for the total revenue from the sale of clocks.
(c) Determine the profit function () for the profit from the sale of clocks.
(d) What profit or loss the company incurs during the first month when all the 1500 clocks are
sold?
(e) Determine the break-even point

Answer 1

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