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Widgets

by sampath » Wed Aug 17, 2011 2:37 am
Two types of widgets, namely type A and type B, are produced on a machine. The number of machine
hours available per week is 80. How many widgets of type A must be produced?
(1) One unit of type A widget requires 2 machine hours and one unit of type B widget requires 4
machine hours.
(2) Every week, at least 10 units of type A widgets and at least 15 units of type B widgets must be
produced
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by rppala90 » Wed Aug 17, 2011 5:52 am
M - number of machine hours needed for 1 type A.
N - number of machine hours needed for 1 type B.
80 = (M * A) + (N * B)

Here M & N can be fractions as they represent time.
A & B have to be positive integers.

(1) M = 2 and N = 4.
80 = 2A + 4B ==> 40 = A + 2B.
Not SUFFICIENT. Two variables, 1 equation.
Strike AD
(2) A >= 10 B >= 15.
80 = M (10) + N(15)
Not SUFFICIENT. Two variables, 1 equation.
Strike B.
(1) & (2)
M = 2 and N =4.
A >= 10 and B >=15.
80 = (M * A) + (N * B)
80 = (2 * 10) + (4 * 15) (least possible values of A and B)
= 20 + 60. ( As A and B must be integers only and incresaing value of A will force decreasing value in B; but B must be greater than or equal to 15).
A must be 10 and B must be 15 to satisfy all the conditions.

Hence answer is C[/spoiler]
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