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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

Optimization : Standard Conjugate Gradient Algorithm

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

Linear optimization business problem

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

Setting up constraints for profit maximization.

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

Optimization problems dealing with minimizing the weight of a tank.

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

4 Questions - Linear Programming and Optimization Problems

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

Determining measurements for perimeter maximization.

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.