### Duality in piecewise linear convex optimization

(See attached file for full problem description) Hint: Consider the linear program: Min v St. Ax-ve <= b Where X is in Rn and v is in R

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(See attached file for full problem description) Hint: Consider the linear program: Min v St. Ax-ve <= b Where X is in Rn and v is in R

The value of good wine increases with age. Thus if you are a wine dealer, you have the problem of deciding whether to sell you wine now, at a price of $P a bottle, or sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of wine t years from now is $P(1+20(sqr(t))). Assu

A. Solve X2 +X + 1 - √(X2 + 3X + 1) = 8 b. Find b such that f(X) = -4X2 + bx +3 the maximum value of 50.

Find the optimal solution for the following problem: TO FROM Chicago Atlanta supply St louis 40 63 250 Richmond 70 30 400 demand 300 350 650

3. (Rootfinding and Optimization) (a) Suppose that f is differentiable on [a, b]. Discuss how you might use a rootfinding method to identify a local extremum of f inside [a, b]. (b) Let f(x) = logx ? cosx. Prove that f has a unique maximum in the interval [3,4]. (NB: log means natural logarithm.) (c) Approximate this local ma

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)

Find the relative maxima and minima of f(x)=x^4-8x^3+22x^2-24x+20.

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

Find the area of the largest rectangle that can be inscribed in a semicircle of radius r. A can in the shape of a right circular cylinder is to be made to hold 1 L of oil. Find the dimensions of the can that will minimize the cost of the metal to manufacture the can. Find the point on the parabola y^2 = 2x that is clo

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

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

Calculate ROR.... (see attachment for full questions) I need to get some outline on a step by step method to solve the problem(s). Some of them involve optimisation.

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

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

F(x)=ln((x^4)+27) (a)Find the intervals of increase and decrease. (b)Find the local maximum and minimum values. (c)Find the intervals of concavity and inflection points. (d)Use the information from (a)-(c) to sketch the graph.

(a) Find all the critical points of f = xy + yz - zx + xyz (Hint: set f = 0) (b) Classify the critical point of f as local maximum, local minimum or saddle points

1. Determine where the function f(x)= 1/(x^2-x) is continuous. (See attachment for full questions)

Locate all relative (local) and absolute maxima and minima for the function: f(x)=2x^5-5x^4+7 on the closed interval [-1,3/2].

Consider the following function f(x)=2sinx-cos2x on the closed interval [0,2pi]. Task: Find all relative (local) and absolute maxima and minima for the function listed above.

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).

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.

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

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

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?

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?

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?

The attached file contains a dynamic problem. I don't think I have it set up right because I keep going in circles when I attempt to solve it. Could you please help me? I am not sure where I am making my mistake.

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?

I have been trying to solve the following problem. Maximize z=x-y subject to: x^2+y^2<=1 The attached file has the work I have done so far. I can't seem to reach plausible solutions.

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