Exam 13: Nonlinear Models:dynamic, Goal, and Nonlinear Programming

What are detrimental deviations?

Without writing equations, what are the basic components to the Kuhn-Tucker conditions for a maximization problem with "?" constraints?

One solution approach for solving a dynamic programming model is a backwards recursion approach.

Can a dynamic programming approach be used to solve a production/inventory problem possessing an infinite planning horizon?

Terrestrial Telescope manufactures the Orion telescope at its Ohio plant.It has been determined that the number of telescopes it can make weekly is a function of the amount of its $20,000 weekly budget allocated to salaries, X₁, and to equipment, X₂.When X₁ and X₂ are expressed in $1,000's, an economic study has shown that the number of telescopes produced can be expressed as the concave function $- 2 X _ { 1 } ^ { 2 } + 24 X _ { 1 } - 2 X _ { 2 } ^ { 2 } + 48 X _ { 2 } + 2 X _ { 1 } X _ { 2 }$ .No more than $15,000 of its weekly budget will be spent on machines. A.Formulate a nonlinear programming model to maximize the weekly production of Orion telescopes. B.Write the Kuhn Tucker conditions for this problem.Are they necessary conditions for optimality? Sufficient? (Since the objective function is concave and the constraints are linear, this is a convex programming model.Thus the Kuhn-Tucker conditions will be both necessary and sufficient.Using Y₁, Y₂, Y₃, and Y₄ to represent the shadow prices

It costs Extel $25 per chip to make its E86 chip used in notebook and other personal computers.Extel can sell all the chips it manufactures using a unit pricing model of ($60 - $0.01X) where X is the daily production of the chip.Fixed daily production costs are $700.A.Formulate an unconstrained nonlinear model that models Extel's daily profit for its E86 chip. B.What should be Extel's daily production of the chip, its price, and the daily profit from producing the chip? C.Suppose its capacity to make chips is limited to 2000 per day. What should be Extel's daily production of the chip, its price, and the daily profit from producing the chip? D.Suppose its capacity to make chips is limited to 1500 per day. What should be Extel's daily production of the chip, its price, and the daily profit from producing the chip? E.Write the Kuhn-Tucker conditions for the model for part D, and show that your solution satisfies these conditions.

In goal programming, the weights assigned to deviations from goals:

Which of the following is true about the optimal solution to a general nonlinear model?

How can you convert a dynamic program to a network model?

A college student has five full days until his next, and last, final exam.While he feels the need to study heavily for the test, he also needs to put in time on his job to pay living expenses.His job pays $6.25 per hour, and daily he can work as many or as few hours as he wishes.He figures that each hour he spends studying, daily, will contribute 10 points to his final exam score.To maintain his scholarship, he must achieve at least an 85 on the exam.(Of course, he must score at least 50 to avoid failing the course.) Also, to stay abreast of his bills, he would like to earn $50 daily.A quick calculation verifies that he will need 16.5 hours a day to meet both objectives.Failing the course is to be avoided, at all costs.However, he believes he can devote only 14 hours daily to the two endeavors. A.Formulate this as a goal programming problem, where achieving an 85 exam score is twice as important as earning $50 daily. B.What should the student do?

Altering the order of the stages of a dynamic program will produce a different result.

If, in a nonlinear programming model classified as convex, the goal is to maximize a concave objective function, why is it referred to as a convex problem? What would happen if the objective function were convex?

Which of the following may be said to have no single form?

In goal programming, deviation variables, E₁ and U₁:

In applying Bellman's principle of optimality for dynamic programming using backwards recursion for a maximization problem, at a given state within a given stage:

The "knapsack problem" may be solved using a __________ programming technique.

While the optimal solution to a constrained nonlinear model need not occur at an extreme point, it must occur at a boundary point.

Efficient solution procedures, guaranteed to provide optimal solutions, exist for convex programming and quadratic programming.

How can we investigate minor changes to the parameters of a dynamic programming problem?

A goal programming problem can be transformed into a series of linear programming problems, each of which has a different objective function and one more constraint than the previous one in the series.