Maximize the objective function: M=6x+3y Under the constraints: Answer a. No maximum exists b. c. (10,0) d. (8, 0)

Expert Answers
sciencesolve eNotes educator| Certified Educator

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.

jeew-m eNotes educator| Certified Educator

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.