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Optimization

Optimization

If a company has m hours of machine time and w hours of labor, it can produce 3m^(1/3)w^(2/3) units of a product. Currently, the company has 216 hours of machine time and 1,000 hours of labor. An extra hour of machine time costs $100, and an extra hour of labor costs $50. If the company has $100 to invest in purchasing addition

Fire department staffing schedule optimization

A fire dept. says that they must have full time firemen work on different days of the week. they must have 10 on mon, 11 on tues, 12 on wed, 13 on thurs, 14 on fri, 15 on sat and 16 on sun . each fireman must work 5 (any 5) consecutive days and then have two days off. but sometimes they can work one day a week OT. each fireman i

Transportation, Transshipment, and Assignment Problem

I need help trying to find the answer. I have tried about 20 different constraints and all of them are wrong. I don't know what I am doing wrong. Some of the constraints that I have tried are x4 + x6 = 175 and x6 + 0 = 175 just to give you an idea of the way that I am thinking. Evidently it is wrong. Please guide me in the

Determining Maximum Profit

Sue and Joan are making cloth pins for a craft show. They have enough fabric to make at most 40 giraffe pins and 80 frogs. They know they will be able to sell at least 20 giraffes and 60 frogs. However, they have time to make only a total of 110 pins. If their is $4.90 for each giraffe and $1.25 for each frog, what is their maxi

Optimization

Specify whether the following statements are true or false and justify your answer. a) Suppose we have an optimal basic feasible solution for an LP in standard form. If we increase the cost of a non-basic variable xn, the current solution will always remain optimal. b) Suppose we have an optimal basic feasible solution for

Optimization Problems/ Newtons Method

--- 4) Find a positive number such that the sum of the number and its reciprocal is as small as possible 6) Find the dimensions of a rectangle with area 1000m^2 whose perimeter is as small as possible 10) A box with square base and open top must have a volume of 32,000cm^3. Find the dimensions of the box that minimize

Max/min/crit point values

(See attached file for full problem description) --- 1) Let F(x) = 2√X - X A. Find the local maximum and minimum values of F (x) in the interval [0,9] B. Determine whether F(x) satisfies al the conditions of MVT in the interval [0,9]. If f(x) satisfies the condition of MVT determine the 'c' value that satisfies th

Optimization Problem using Excel add-in Solver

This problem requires the use of Excel and the add-in, called Solver. The course is Excel-based and Solver is the optimization application used for all problems. This particular problem comes from Cliff Ragsdales's " Spreadsheet Modeling and Decisoin Analysis" and is case problem 6.3. The problem appears in this text box an

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