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
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
A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation cost are: Destination Assembly Plant 1 2 3 Supply Source A 5 9 16 200 Factory B 1 2 6 400 C 2 8 7 200 Demand 120 620 60 What are the t
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
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
Find the maximum and minimum values of this function: G= 7X+16y subject to 7x+3y is less than or greater to 37 x is greater than or equal to 0 y is greater than or equal to 0
Find critical numbers, inflection points, absolute max and absolute min values for the following given functions:
Find critical numbers, inflection points, absolute max and absolute min values for the following functions: (a) f(x) = sqrt(x^2-8x+32) * (x-4) (b) f(x) = x*sqrt(x^2+4)
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
--- 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
(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
Problem: A furniture manufacturer has warehouses in cities represented by nodes 1, 2, and 3 in Figures 5.34. The values on the arcs indicate the per unit shipping costs required to transport living room suites at each warehouse is indicated by the negative number next to nodes 1, 2, and 3. The demand for living room suites is
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. The problem appears in this text box and is also attached as a MS Word file, so it is sure to transmit legibl
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
(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
Optimization Problems : Largest Recatangle in a Semicircle, Minimizing Area Given Volume and Finding the Point on a Parabola Closest to Another Point
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)