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 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?
The management of a large store wishes to add a fenced-in storage yard of 20,000 square feet, using the building as one side of the yard. Find the minimum amount of fencing that must be used to enclose the remaining 3 sides of the yard.
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.