--- 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 the co
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
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
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
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
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
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
This spring I want to plant a garden on a 10x20 feet of land. The rows are each 10 feet long. I want to plant tomatoes, corn and green beans. The corn and tomatoes rows will be 2 feet wide each. The green beans will each be 3 feet wide. On a scale of 1 to 10 (10 being the best) I would place tomatoes at 10, corn at 7, and b
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
Please see the attached file for the fully formatted problems. We consider the function J defined as and . 1) Prove mathematically that K is strictly convex. 2) Descibe the two algorithms of conjugated gradient for this function K. 3) Are they descending algorithms? 4) Choose one of them, and choose a method to
Please see the attached file for the fully formatted problems. Let be defined for as: 1) Evaluate (upside down Delta) Jx. 2) Calculate HessJx . 3) Prove mathematically that J has a unique minimum. 4) a) We are given . Describe the algorithm of the gradiant of optimal step for this function J. b
A) Make a table that summarizes the above information. b) Write down the optimization equation and the constraint equations and label them as such. Make sure your write down all of the constraint equations. c) Graph, either by hand or using Excel, the constraint equations. Identify the feasible region. Make sure to labe
A florist is planning to make up floral arrangements for the upcoming holiday weekend. He has following supply of flowers in stock this Friday and he cannot get any more. Type------Number available------Cost per flower Roses----------800-----------------------0.20 Carnations---4000----------------------0.15 Gardenias
Your iron works has contracted to design and build a 500-cubic foot, square based, open topped, rectangular steel holding tank for a paper company. The tank is to be made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that wi
You have 80 inches of wire. You can break it into two pieces or leave it intact. You're going to bend the pieces into squares. What are the maximum and minimum possible total areas of these squares?
A cook is puzzling over the number of pounds of food he should purchase in order to minimize his cost. He has always brought his food from a small health food store in town. The store sells two types of mixtures. Both of these mixtures contain the three ingredients needed, but the cook needs his own special ratio of these ing
An architect is designing an office building that is 120 feet by 72 feet. The architect wishes to use prefabricated rectangular panels to construct the outside walls. If the same size panels are to be used on all sides of the building what is the widest panel that can be used? Explain your reasoning.