Optimization: Finding the minimum amount of fencing using implicit differentiation.
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.
Optimization: Finding the maximum area using implicit differentiation.
A farmer has 160 feet of fencing to enclose 2 adjacent rectangular pigpens. What dimensions should be used so that the enclosed area will be a maximum?
Working with the Kuhn-Tucker Condition.
Verify that x^=(1,3) is a K_T point of the following problem. Min f(x,y)=(x-1.5)^2+(y-5)^2 st. g1(x,y)=-x+y<=2 g2(x,y)=2x+3y<=11 g3(x,y)=-x<=0 g4(x,y)=-y<=0
Working with the Lagrangian Dual problem.
Form the Lagrangian Dual problem of the following quadratic programming: Minimize 1/2x'Hx+d'x subject to Ax<=b Where H is symmetric and positive definite.
Linear Programming Problem: Maximizing Productivity
The two products that case chemical makes- cs01 and cs02 yield excessive amounts of three different pollutants: a,b,and c. the state government has ordered the company to install and to employ antipollution devices. the following table provides the current daily emissions in kg/1000liters and the maximum of each pollutant allowe ...continues
Functions: K-T (Kuhn-Tucker) Condition
Consider the following program: Maximize f(x,y)=x^2+4xy+y^2 subject to g(x,y)=x^2+y^2-1=0
Investment Linear Programming model: Risk Management
Please see attachement for more clear format. The portfolio Manager of Pension planners has been asked to invest $1,000,000 of a large pension fund. The investment research development department has identified six mutual funds with varying investment strategies, resulting in different potential returns and associated risks, ...continues
Optimization/Minimizing Total Expense
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 ...continues
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 ...continues
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 ...continues
