Optimization 1 October 28, 2016 1 Optimization 1 October 28, 2016 - PDF document

Optimization 1 October 28, 2016 1

Optimization 1 October 28, 2016 Of all rectangles with a perimeter of 20ft, find the dimensions of the one with the largest area. 2

Optimization 1 October 28, 2016 1. Draw and label the picture of the problem 2. Find a formula for the objective function 3. Identify constraints to eliminate extra variables 4.Find the interval of interest 5. Find the absolute max/min using calculus 3

Optimization 1 October 28, 2016 We are fencing in a field adjacent to a large barn. We split the fenced area into 2 plots by a fence pe rpendicular to the barn. If we want the total area fenced in to be 200 sq m, what are the dimensions to minimize the amount of fence necessary? 4

Optimization 1 October 28, 2016 A box with square base is designed to have a volume of 16 cu ft. The material to make the base costs twice as much (per sq ft) as the material for the sides, and the material in the top costs half as much as the sides. What are the dimensions of the box to minimize the material cost? 5

Optimization 1 October 28, 2016 A Norman window has the shape of a rectangle surmounted by a semicircle. A certain Norman window is to have a perimeter of 20 ft. What is the largest possible area? 6

Optimization 1 October 28, 2016 The manager of a 100 unit apartment complex knows that all of her units will be occupied if the rent is $800/month. A market survey shows that for each $10 /month increase in rent, 1 additional unit will be vacant. What rent will maximize revenue? 7

Optimization 1 October 28, 2016 A rectangular pool with an area of 50 sq m is surrounded by a wooden walkway 1 m wide on two opposite side, and 2 m wide on the other two sides. What dimensions of the pool minimize the area of the walkway? 8