Optimization Problems Homework Answers - 5.6 Solving

A cylindrical can must hold $100\pi$ cubic inches of soda. The metal for the top and bottom costs twice as much per square inch as the sides. Find the radius that minimizes cost.

Graphing the constraints, we get:

. These values are your candidates for the maximum or minimum. 5. Verify the extremum 5.6 solving optimization problems homework answers

To solve section 5.6 homework problems, you must to find the critical points that represent the optimal solution.

A farmer has 100 acres of land to plant two crops, wheat and corn. The profit from wheat is $200 per acre, and the profit from corn is $300 per acre. The farmer has a limited amount of water, which is 2000 gallons. Wheat requires 20 gallons of water per acre, and corn requires 30 gallons of water per acre. Find the optimal number of acres to plant wheat and corn to maximize profit. A cylindrical can must hold $100\pi$ cubic inches of soda

If you're stuck on a specific homework problem, follow this repeatable framework: 1. Understand and Label

There are several types of optimization problems, including: Graphing the constraints, we get:

2x + 3y ≤ 240 x + 2y ≤ 180 x ≥ 0 y ≥ 0

Profit = 10x + 15y

A power line runs along a straight road. A factory is 2 miles from the road and 5 miles down the road from the nearest connection point. It costs $10,000 per mile to run cable underground and $6,000 per mile to run cable overhead along the road. Find the optimal point to switch from overhead to underground to minimize cost.

If you’re stuck on a specific problem and need the for your exact textbook (e.g., Calculus: Early Transcendentals 9th ed. by Stewart, problems 11–28), use the method above, not just the back-of-book number. The real skill is setting up the equations.