- #1
ssd
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Homework Statement
Given a,b,c real and a^2+b^2 +c^2=1, to find the minimum of c(3a+4b)
Homework Equations
The Attempt at a Solution
No positive clue yet.
ssd said:Homework Statement
Given a,b,c real and a^2+b^2 +c^2=1, to find the minimum of c(3a+4b)
Homework Equations
The Attempt at a Solution
No positive clue yet.
ssd said:Thanks all for your kind suggestions. The Lagrangian multiplier solves the problem.
ssd said:The result is a=-1/2, b=-1/2, c=1/√2 as per my calculations.
Since this is in the homework section, I can't give you my solution. Like I asked, walk me through how you arrived at your solution and we will critique it.ssd said:Surely I shall check my calculations. Notwithstanding though, when it is -2.5?
The term "minimum" refers to the smallest possible value that can be obtained for the expression c(3a+4b) while still satisfying the given condition a^2+b^2+c^2 = 1.
To solve for the minimum, we can use the method of Lagrange multipliers. This involves setting up a system of equations using the given expression and the constraint a^2+b^2+c^2 = 1, and then solving for the values of a, b, and c that satisfy these equations.
There is no specific formula for finding the minimum in this case, as it depends on the specific values of a, b, and c that satisfy the given constraint. However, the method of Lagrange multipliers provides a systematic approach for solving for the minimum value.
Yes, the minimum value of c(3a+4b) can be negative depending on the values of a, b, and c. This is because the given expression does not have any restrictions on the sign of the variables a, b, and c.
Yes, this type of problem can be seen in various fields such as economics, engineering, and physics. For example, in economics, this type of problem can be used to find the minimum cost for producing a certain quantity of goods. In physics, it can be used to find the minimum energy required to achieve a certain motion or state.