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 allowed in kg. pollutant======cs01========cs02=====max allowed A ============ 25 ========40 ====== 43 B ============ 10 ======== 15 ======20 C ============ 80 ======== 60 ======50 the manager of the production department has approved the installation of two antipollution devices. the emissions from each product can be handled by either device in any proportion... click for more