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Find the minimum value c=x+3y

Find the minimum value c=x+3y-example-1

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Answer: To find the minimum value of c = x + 3y, you need to solve the optimization problem with a constraint or without any constraint.

Without a constraint:

The minimum value of c = x + 3y without a constraint is achieved when the partial derivatives of c with respect to x and y are equal to zero.

Let's take the partial derivative of c with respect to x:

dc/dx = 1

And with respect to y:

dc/dy = 3

Setting these equal to zero, we have:

1 = 0 and 3 = 0

Since the partial derivatives are not equal to zero, there is no minimum value of c without a constraint.

With a constraint:

If there is a constraint, such as a limit on x or y, then the minimum value of c can be found by using optimization techniques, such as the method of Lagrange multipliers.

Explanation:

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