Optimization DY0-001 Practice Questions (Page 3)

Questions 11–15

1. 11foundation · easy

   Which of the following is a typical example of an unconstrained optimization problem?

   • AMinimizing cost while ensuring that all customer demands are met
   • BMaximizing profit subject to a production capacity limit
   • CFinding the shortest path in a graph with edge weights
   • DMinimizing a quadratic function over all real numbers
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2. 12foundation · easy

   How does constrained optimization generally compare to unconstrained optimization in terms of complexity?

   • AUnconstrained optimization is typically more complex because it must search the entire domain
   • BConstrained optimization is simpler because constraints narrow the search space
   • CBoth are equally complex because they use the same algorithms
   • DConstrained optimization is typically more complex because it must find a solution within a restricted feasible region
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4. 13application · medium

   A retail chain wants to minimize total shipping costs for its weekly deliveries. Each warehouse has a fixed capacity, and each store has a minimum demand that must be met. The logistics team needs to determine how many units to ship from each warehouse to each store. Which type of optimization problem is this, and what is the key characteristic that makes it so?

   • AUnconstrained optimization, because the goal is to minimize a cost function without any restrictions on the decision variables.
   • BConstrained optimization, but only because the problem involves multiple warehouses and stores, which adds complexity.
   • CUnconstrained optimization, because the shipping cost function alone determines the optimal solution, and the capacities and demands are just data inputs.
   • DConstrained optimization, because the solution must respect the fixed capacities of warehouses and the minimum demands of stores.
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5. 14foundation · easy

   Which technique is commonly used to solve constrained optimization problems?

   • ALagrange multipliers
   • BGradient descent
   • CRandom search
   • DNewton's method
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6. 15application · medium

   A data scientist is tuning a machine learning model's hyperparameters to minimize validation error. The team has no specific business requirement that limits the range of the hyperparameters, and the only goal is to find the single best-performing combination. Which optimization approach is most appropriate, and why?

   • AUnconstrained optimization, because the search space is not limited by any external business rules or operational constraints.
   • BConstrained optimization, because hyperparameters always have a finite range defined by the model's implementation.
   • CUnconstrained optimization, but only if the model is a linear model, otherwise it is constrained.
   • DConstrained optimization, because the validation error itself is a constraint that the model must satisfy.
   Reveal Solution Discussion Select an answer first