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Ask by Hampton Zimmerman. in the United States
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The minimum value of is when and .

Solution

To minimize the function , we need to consider the constraints that define the feasible region for and . However, since no constraints are provided in your problem, I will assume that and can take any non-negative values (i.e., and ).
  1. Identify the function to minimize:
  2. Determine the behavior of the function:
    • The function is linear, and its minimum value occurs at the boundary of the feasible region.
    • Since both coefficients (6 and 7) are positive, decreases as and decrease.
  3. Evaluate the minimum:
    • The minimum value occurs at the point where both and are at their lowest values, which is and .
  4. Calculate the minimum value:
Thus, the minimum value of is at the point .
If there are specific constraints you would like to include, please provide them for a more detailed analysis.

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Bonus Knowledge

To minimize the objective function , you’re generally solving an optimization problem, often seen in linear programming. The key here is to define constraints that limit the values of and . Once you have your constraints, you’d typically graph the feasible region, identify corner points, and evaluate at those points to find the minimum.
For a real-world application, say you’re managing resources in a factory, where might represent the number of product A made, and the number of product B. By minimizing , you’re reducing costs while ensuring you meet production requirements. This approach can help enhance profit margins by avoiding unnecessary expenditure.

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