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Optimization

Proof of Dual using Farkas Lemma (PhD)

Hello, Could you please help me to prove this using Farkas Lemma? Well, I initially thought that I can use Farkas Lemma, but if it is impossible to use the lemma (though I do belive it will help), you might try other way. Thank you! --- (See attached file for full problem description)

Optimization Modeling In Excel (using Solver)

A marketing research group needs to contact at least 150 wives, 120 husbands, 100 single adult males, and 110 single adult females. It costs $2 to make a daytime call and (b/c of higher labor costs) $5 to make an evening call. Because of the limited staff, at most half of all phone calls can be evening calls. Determine how to

Interpreting LINDO output in linear programming optimization

Based on the attached file, please anwer: a. Give the complete optimal solution b. What constraints are binding? c. What would happen if the coefficient of X1 is increased by 6? d. What would happen if the right-hand-side value of constraint 1 decreased by 10? e. Which right-hand-side would you be most intereste

Interpreting LINDO Output in Linear Programming Optimization

Based on the attached file, please anwer: a. Give the complete optimal solution b. What constraints are binding? c. What is the dual price for the second constraint? d. Over what range can the objective function coefficient X2 vary before a new solution point becomes optimal? e. What would happen if the first constra

Applied differentation/optimization

It may be the mental picture that's confusing me, but I can't figure this one out: "A painting in an art gallery has height h and is hung so that its lower edge is a distance d above the eye of an observer. How far from the wall should the observer stand to get the best view? (In other words, where should the observer stand

Research Works for Satellite Route Optimization.

The Satellite Mission Scheduling problem with Dynamic Tasking (SMS-DT) involves scheduling tasks for a satellite, where new task requests can arrive at any time, non-deterministically, and must be scheduled in real-time. The schedule is a time ordered sequence of activities (scheduled tasks) to be performed by the payload of a s

Local and Absolute Maxima and Minima

Locate all relative (local) and absolute maxima and minima for the function: f(x) = x^2/x^2+1 over the entire graph (negative infinity, positive infinity).

Maximize demand

The area of a closed box is 200 square inches. If the box has a square base, find the length of the base that will maximize the volume.

Maximum and minimum

Consider the minimization of *see attached for equation* subject to the constraint of *see attached for equation* (a) Graph the contour point of with y-axis and x-axis between -2 and 6.(on my paper there is a dot (between point (3,3) Estimate where extrema values may occur and compute the function values correspondi

Critical Points, Max-Min values, inflection points

Given: y = f(x) = 3x4 + 4x3 Find: A. All critical points B. Max - Min Values C. Inflection points D. Where is f(x) concave up E. Where is f(x) concave down F. X and Y intercepts G. Where f(x) is increasing H. Where f(x) is decreasing I. Sketch the curve label

Optimization of business and economics

A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of the page are to have 1.5 inches, and the margins on the left and right are to be in 1 inch. What should the dimensions of the page be so that the least amount of paper is used?

Optimization

A wire 10 feet long is to be cut into two pieces, each of which is to formed into a square. What is the largest possible total area of the two squares? What is the smallest possible total area?

Random Number Generator

For the equation RAND = (ac+m)MOD MAX , if the set of random numbers is known, is it possible to calculate a,c and m?

Dynamic Programming - The Allocation Problem

Please see the attached file for the fully formatted problems. The beginning appears below... Example Problem: A sales manager has 3 areas and 5 sales engineers. If the assignment of sales engineers to areas will result in the expected sales as shown, how should the engineers be assigned to maximize sales?

Optimization

Please see the attached file for full problem description. --- Problem 1 In deciding whether to set up a new manufacturing plant, company analysts have decided that a linear function is a reasonable estimation for the total cost C(x) to produce x items. They estimate the cost to produce 10,000 items as $547,500 and the cos