Question 63

Consider the four variables A, B, C and D and a function Z of these variables, $$Z = 15A^2 - 3B^4 + C + 0.5D$$ It is given that A, B, C and D must be non-negative integers and thatall of the following relationships must hold:
i) $$2A + B \leq 2$$
ii) $$4A + 2B + C \leq 12$$
iii) $$3A + 4B + D \leq 15$$
If Z needs to be maximised, then what value must D take?

Solution

To maximize Z, B has to be minimized and A,C,D are to be maximised.

The value of B can be 0 or 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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