Question 1

Nonlinear programming problems with decreasing marginal returns are generally easier to solve then nonlinear programming problems with increasing marginal returns.

Accepted Answer

Nonlinear programming problems with decreasing marginal returns often exhibit concavity in their objective functions, making them easier to solve due to the presence of a single global optimum. In contrast, problems with increasing marginal returns can have convex objective functions, potentially leading to multiple local optima and making the solution process more complex.

Question 2

Sometimes the Solver can return different solutions when optimizing a nonlinear programming problem.

Accepted Answer

This is true because nonlinear programming problems can have multiple local optima, meaning there are multiple solutions that are optimal locally but may not be globally optimal. The Solver algorithm may converge to different local optima depending on the initial starting point or the specific optimization method used.

Question 3

A local maximum is always a global maximum in a nonlinear programming problem.

Accepted Answer

A local maximum is only the highest point in a small area of the feasible region, but it may not be the highest point in the entire feasible region. Therefore, a local maximum is not always a global maximum in a nonlinear programming problem.

Question 4

Having activities with decreasing marginal returns is the only way that the proportionality assumption can be violated.

Accepted Answer

The proportionality assumption can be violated not only through activities with decreasing marginal returns but also through increasing marginal returns, non-constant returns, or any situation where outputs do not change proportionally with inputs.

Question 5

In separable programming,if an activity violates the proportionality assumption it must have increasing marginal returns.

Accepted Answer

If an activity violates the proportionality assumption, it does not necessarily imply increasing marginal returns. It could also have decreasing marginal returns, constant marginal returns or even non-monotonic marginal returns.

Question 6

If C1 is a changing cell,then ROUND(C1)is a linear function.

Accepted Answer

ROUND is a non-linear function as it rounds up or down based on the decimal value of the input. Therefore, the output is not proportional to the input and hence not a linear function.

Question 7

If D1 is a data cell,and C1 and C2 are changing cells,then IF(D1 >= 2,C1,C2)is a linear function.

Accepted Answer

The answer of If D1 is a data cell,and C1...

Question 8

In separable programming,each activity that violates the proportionality assumption is separated into parts with a new variable for each part.

Accepted Answer

This statement is correct. Separable programming involves separating activities that violate the proportionality assumption into parts, each with a new variable representing the amount of that part. This allows for the optimization of each part separately, while still maintaining the overall constraints of the problem.

Question 9

A quadratic programming problem is a special type of linear programming problem.

Accepted Answer

A quadratic programming problem involves optimizing a quadratic function subject to linear constraints, while a linear programming problem involves optimizing a linear function subject to linear constraints.

Question 10

Separable programming is applicable when there are increasing or decreasing marginal returns.

Accepted Answer

Separable programming is used for optimization problems where the objective function and constraints can be broken down into parts that depend on individual variables. It does not specifically relate to increasing or decreasing marginal returns, but rather to the mathematical structure of the problem.

Question 11

Applying separable programming requires having profit graphs that are smooth curves.

Accepted Answer

Separable programming is used for optimization problems where the objective function and constraints can be expressed as sums of functions that depend on individual variables. This technique does not require profit graphs or any other functions to be smooth curves; it is applicable to problems where these functions can be broken into separate parts, regardless of their smoothness.

Question 12

When the marginal return from an activity decreases on a continuous basis,the profit graphs will consist of a series of line segments.

Accepted Answer

When the marginal return decreases on a continuous basis, the profit graphs will consist of a smooth, downward-sloping curve, not a series of line segments.

Question 13

In problems where the objective is to minimize the total cost of the activities,an activity is said to have decreasing marginal returns if the slope of its cost graph never increases but sometimes decreases as the level of the activity increases.

Accepted Answer

The answer of In problems where the objective is to...

Question 14

Excel's curve fitting method is used to graph a nonlinear equation.

Accepted Answer

The answer of Excel's curve fitting method is used to...

Question 15

Excel's curve fitting method is used to find the values of the parameters for an equation that best fit data.

Accepted Answer

Excel's curve fitting method is designed to find the best-fit values of parameters for an equation that matches the given data.

Question 16

A nonlinear function may contain a product of two variables.

Accepted Answer

A product of two variables, such as xy, is a common form of a nonlinear function.

Question 17

Linear programming assumes that the profit from each activity is proportional to the level of that activity.

Accepted Answer

Linear programming involves maximizing or minimizing an objective function while satisfying a set of constraints. The objective function is typically a linear combination of decision variables, where each decision variable represents the level of a certain activity. In this context, it is assumed that the profit or cost associated with each activity is directly proportional to the level of that activity. For example, if producing x units of a product generates a profit of $100, then producing 2x units would generate a profit of $200.

Question 18

If the slope of a graph never increases but sometimes decreases as the level of the activity increases,then it is said to have decreasing marginal returns.

Accepted Answer

True, this is the definition of decreasing marginal returns in economics.

Question 19

In some cases of separable programming,the profit graphs will be curves rather than a series of line segments.

Accepted Answer

This is true. In some cases, the profit function may not be linear, and therefore the profit graph will not consist of a series of line segments. However, if the profit function is still separable, then separable programming techniques can still be applied.

Question 20

If C1:C6 are all changing cells,then SUMPRODUCT(C1:C3,C4:C6)is a linear function.

Accepted Answer

SUMPRODUCT is a non-linear function because it involves multiplying the values in the two arrays and then summing them up. This multiplication operation makes the function non-linear.

Quiz 8: Nonlinear Programming