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Exam 8: Nonlinear Optimization Models

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Question 31

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A convex function is

A) bowl-shaped up.
B) bowl-shaped down.
C) elliptical in shape.
D) sinusoidal in shape.

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Question 32

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Skooter's Skateboards produces two models of skateboards, the FX and the ZX. Skateboard revenue (in $l,000s) for the firm is nonlinear and is stated as (number of FXs)(5 − 0.2 number of FXs) + (number of ZXs)(7 − 0.3 number of ZXs). Skooter's has 80 labor-hours available per week in its paint shop. Each FX requires 2 labor-hours to paint and each ZX requires 3 labor-hours. Formulate this nonlinear production planning problem to determine how many FX and ZX skateboards should be produced per week at Scooter's.

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FX = number of FX skateboards ...

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Question 33

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MegaSports, Inc. produces two high-priced metal baseball bats, the Slugger and the Launcher, that are made from special aluminum and steel alloys. The cost to produce a Slugger bat is $100, and the cost to produce a Launcher bat is $120. We can not assume that MegaSports will sell all the bats it can produce. As the selling price of each bat model -- Slugger and Launcher -- increases, the quantity demanded for each model goes down. ​ Assume that the demand, S, for Slugger bats is given by S = 640 − 4P_S and the demand, L, for Launcher bats is given by L = 450 − 3PL where P_S is the price of a Slugger bat and P_L is the price of a Launcher bat. The profit contributions are P_S S − 100S for Slugger bats and P_L L − 120L for Launcher bats. Develop the total profit contribution function for this problem.

Which of the following is not true regarding a concave function?

Any feasible solution to a blending problem without pooled components is feasible to the problem with pooled components.

Nonlinear programming algorithms are more complex than linear programming algorithms.

A feasible solution is a global optimum if there are no other feasible solutions with a better objective function value in the immediate neighborhood.

A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.

​Describe how the Markowitz portfolio model can be modified to account for upper and lower bounds being placed on the amount of an asset type invested in the portfolio.

An investor can pick the mean-variance tradeoff that he or she is most comfortable with by looking at a graph of the

Any feasible solution to a blending problem with pooled components is feasible to the problem with no pooling.