The management of a large store has 800 feet of fencing to fence in a rectangular storage yard using the building as one side of the yard. If fencing is used for the remaining sides, find the area of the largest possible yard. A long sheet of metal, one foot wide(12 inc) is to be turned up at both sides to make a horizontal g
--- 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
The concentration C of a certain drug in a patient's bloodstream t minutes after injection is given by C(t)=50T divide by t^2 +25 a) Using your graphing utility, graph C=C(t). b) Determine the time at which the concentration is highest. c) Find the horizontal asymptote of C(t). What happe
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
Car B is 30 miles directly east of Car A and begins moving west at 90 mph. At the same moment car A begins moving north at 60 mph. What will be the minimum distance between the cars and at what time t does the minimum distance occur ?
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
A car travels at a constant speed of 70km per hour for a time of 2 hours and 45 minutes. Its speed is quoted to the nearest km/h and the time is quoted to the nearest minute. Calculate: a) the maximum possible distance that the car could have travelled b) the minimum distance the car could have travelled
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
4. Let a function f be continuous in a closed bounded region R, and let it be analytic and not constant throughout the interior of R. Assuming that f(z) does not equal 0 anywhere in R, prove that f(z)f has a minimum value n in R which occurs on the boundary of R and never in the interior. Do this by applying the corresponding re
A customer has asked me to design an open-top stainless steel vat. It is to have a square base and a volume of 32 cubic ft. to be welded from quarter-inch plate, and to weigh no more than necessary. What dimensions do I recommend?
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. 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 truck driving on the Interstate averages a fuel efficiency of 4 miles per gallon when traveling at 50mph. The truck looses a tenth of a mile per gallon in fuel efficiency for each mile per hour increase in speed. Fuel costs $1.19 per gallon. The trucker is paid $27.50 per hour and fixed costs to run the truck are $11.33 per ho
A farmer has 600 feet of fencing with which to enclose a rectangular plot. What is the maximum area he can enclose? Hint: Find a model for the area of the rectangular plot and maximize by completing the square
A city block, 500 ft by 500 ft has a large building 300ft by 300ft in the exact center. The rest of the block is an unobstructed paved lot. What is the shortest distance from the SW corner to the NE corner of the city block, going through the paved lot?