|TIME: 3 HOURS|
|(i)||Answer all 15 questions.|
|(ii)||Show details of your solutions.|
|(iii)||Calculators are permitted.|
|(iv)||4 points for each question. Total points 60.|
|1.||A manufacturer has a fixed cost of $4000. It costs him $4000 to manufacture 1000 units. He sells them (1000 units) for $6000. Find the cost function, revenue function and break-even point.|
Find the value of (2A)(3B-4C).
||Find the inverse of
||Using Gauss-Jordan elimination method, solve
150x + 120y such that
An owner of a gasoline station can have at most 64,000 litres of
gasoline in his tanks. He estimates that he can sell at least 20,000
litres of regular gas and at least 8,000 litres of premium gas. He
also knows that he cannot sell more than 3 times as much regular gas
as premium gas. If regular gas sells at 55 cents per litre and
premium gas at 60 cents per litre, find his maximum return. EXPRESS
this as a linear programming problem. DO NOT SOLVE IT!!
be the universal set. Let
||100 charitable organizations receive aid from at least one of
the 3 groups A, B or C. 40 from A, 55 from B and 65 from
C, 15 from A and B, 30 from B and C and 20 from A and C.
How many receive aid from all 3 groups?
||From a group of 10 women and 6 men a committee of 5 is to be
formed with the condition that there should be more women than men in
the committee. How many different committees can be formed?
||A box contains 3 red, 5 white and 2 blue balls. Two balls are
picked at random one after another without replacement. What is the
probability that one is blue and the other is red?
||In section A there are 5 boys and 7 girls. In section B
there are 16 boys and 20 girls. A die is rolled. If 1 or 6 comes up
a student is selected at random from section A. If any other number
comes up a student is selected at random from section B. If the
student selected is a girl, what is the probability that she is from
||At end end of 7 years, I need $100,000. How much should I
deposit now in a bank that pays a nominal rate of 9% compounded
||Bank I has a nominal rate of 6% compounded quarterly. Bank
II has a nominal rate of 6.10% compounded semi-annually. Which one
is a better rate?
||Suppose $50 is deposited at the end of each quarter for 10
years, the nominal rate being 8% compounded quarterly. What is the
total at the end of 10 years? How much is the interest earned?
||I borrow $50,000 from a bank whose nominal rate is 7%
compounded yearly. The debt is amortized over a period of 10 years
and each payment is made at the end of each year.
||How much should each payment be?
||What is the outstanding balance at the end of 7 years?