AGEC 3413 Chapter 10 True/False
A firm has a cost function of 3x2 - 25x + 374. Without having two examples of their output volume and total cost, we cannot determine their fixed cost.
FALSE
An optimal solution to a nonlinear programming problem will always occur at the boundary of the feasible solution space formed by the constraint.
FALSE
Both linear and nonlinear programming models have the general form of an objective function subject to more than 1 constraint.
FALSE
Constraints for nonlinear programs are usually nonlinear.
FALSE
Decision variables cannot be multiplied by each other in the objective function of a nonlinear program.
FALSE
If a nonlinear program has been correctly formulated, procedures guarantee a solution.
FALSE
Maximum profit is achieved everywhere the first derivative of the profit function equals zero.
FALSE
The first derivative of a cost function equals zero at the point V = 100. This is definitely the worst output volume for the producer to choose.
FALSE
The slope of a curve at its highest point equals 1.
FALSE
A profit function of Z = 3x2 - 12x + 5 reaches maximum profit at x = 2 units of output.
TRUE
Both linear and nonlinear programming models are examples of constrained optimization models.
TRUE
Classical optimization is the use of calculus to determine the optimal value of a variable.
TRUE
Classical optimization uses calculus to determine the optimal values of a variable.
TRUE
In an unconstrained nonlinear programming problem, we have a single nonlinear objective function and no constraints.
TRUE
In portfolio selection problems, risk is measured by the variance of the return on the portfolio.
TRUE
In solving the facility location problem, the objective is to locate a centralized facility that serves customers or other facilities such that the distance traveled between the facility and customers or other facilities is minimized.
TRUE
The Lagrange multiplier at the optimum gives only the instantaneous rate of change in the objective value.
TRUE
The Lagrange multiplier is analogous to the dual variables in a linear programming problem.
TRUE
The slope of a curve at any point is equal to the derivative of the curve's function.
TRUE