Xavier Aptitude Test 2020 Paper

Question : 63 of 100

Marks: +1, -0

Consider the four variables

\A, \B, \C

and

\D

and a function

\Z

of these variables, It is given that

\A,\B, \C

and

\D

must be non-negative integers and that all of the following relationships must hold:
i)

2\A + \B ≤ 2

ii)

4\A + 2\B +C ≤ 12

iii)

3\A +4\B +\D ≤ 15

If $\Z$ needs to be maximized, then what value must $\D$ take?

Solution:

To maximize

\Z, \B

has to be minimized and

\A,\C,\D

are to be maximized.
The value of

\B

can be

0

1

Case 1:

\B=0 ⇒ \A=1⇒ \C=8

and

\D=12

\Z= 15+8+6=29

Case 2:

\B=1 ⇒ \A=0 ⇒ \C=12

and

\D=15

\Z=-3+12+7.5=16.5

.'. \D=12

is correct answer.

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