Calculus Optimization Worksheet A Rain Gutter Is To Be Constructed

1 a company has started selling a new type of smartphone at the price of 110 0 05 x where x is the number of smartphones manufactured per day.

Calculus optimization worksheet a rain gutter is to be constructed.

Determine what theta should be chosen so that the gutter will carry the most water when it is full. Maximizing or minimizing some quantity so as to optimize some outcome calculus is the principal tool in finding the best solutions to these practical problems. A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one third of the sheet on each side through an angle theta. The parts for each smartphone cost 50 and the labor and overhead for running the plant cost 6000 per day.

Here are the steps in the optimization problem solving process. By bending up one third of the sheet on each side through an angle θ. Thanks to all of you who support me on patreon. Most real world problems are concerned with.

To calculate the area split the cross section of the gutter into two triangles and a rectangle. How should theta be chosen so that the gutter will carry the maximum amount of water. Differential calculus published in vacaville california usa a rain gutter is to be constructed from a metal sheet of width 30 cm. Optimization problems name calculus ab for each of the following define your variables write an equation representing the quantity to be maximized or minimized and solve the problem.

A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one third of the sheet on each side through an angle θ. You da real mvps. We need to begin by constructing a function which gives the area of the gutter in terms of theta. 1 draw a diagram depicting the problem scenario but show only the essentials.

We have step by step solutions for your textbooks written by bartleby experts. Optimization problems practice solve each optimization problem. A rain gutter is to be constructed from a metal sheet of width 30cm by bending up one third of the sheet on each side by an angle theta from the horizontal theta zero represents the unbent sheet. Verify if it is a maximum or minimum using the 2nd derivative test when easy otherwise use the 1st derivative test.