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Maximize the objective function: M=6x+3y Under the constraints: Answer a. No maximum...

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babyryan95 | Honors

Posted July 15, 2012 at 8:48 PM via web

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Maximize the objective function:
M=6x+3y
Under the constraints:

Answer

a.
No maximum exists
b.
c.
(10,0)
d.
(8, 0)

2 Answers | Add Yours

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 16, 2012 at 6:22 PM (Answer #1)

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If you consider M as a contant then there is no exact maximim value.

y= (-6*x-M)/3

Here the maximum is not an exact value. It will be infinity. So we can say the answer is a.

 

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted September 18, 2012 at 5:19 PM (Answer #2)

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You need to maximize the objective function M, hence, you should first write this function in terms of x or in terms of y. You should consider other conditional relation to help the objective function to be expressed in terms of x or in terms of y.

Since the conditional relation misses, you should maximize the given function finding its partial derivatives and setting them equal to zero such that:

`M_x = 6 != 0`  (differentiate with respect to x, considering y as constant)

`M_y = 3 != 0` (differentiate with respect to y, considering x as constant)

Hence, evaluating the partial derivatives yields that the objective function cannot be maximized, under the given conditions.

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