Question

Solve the following problem by Dynamic Programming:
Maximize z = (y1 + 2)^2 + y2 * y3 + (y4 - 5)^2
subject to
y1 + y2 + y3 + y4 <= 5
yi >= 0 and integer, i = 1, 2, 3, 4

Answer 1

problem becomes

Max subject to for which we get

problem becomes

Max subject to for which we get

problem becomes

Max subject to

Which has max value

problem becomes

Max subject to

Which has max value for

problem becomes

Max subject to

If then

If problem becomes Max subject to

Which has max value for

If problem becomes subject to for which max value is 32 again for

If problem becomes subject to for which max value is 41 for

If problem becomes subject to for which max value is 36 for

makes our problem Max subject to

Which has max value

makes our problem Max subject to

Which has max value

Thus, the overall maximum value is attained when

And the value is

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