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5. You are framing a door, in the shape of a rectangle with a semicircle on top (see picture; there is no framing along the dotted line). The rectangle has width r and height y. You plan to use 20 feet of framing. The cost of framing for the straight edges is $2 per foot. The cost of framing for the circular edge is $5 per foot. Write the constraint equation and the objective function for the optimiza- tion problem of finding the minimum cost, using the variables r and which is the objective and which is the constraint. You do not meed to find the minimum cost. y. Mark Reminder: A full circle of radius r has circumference 27r. The radius of a circle is 1/2 of the diameter. You should show some work for this problem.

5. You are framing a door, in the shape of a rectangle with a semicircle on top (see picture; there is no framing along the dotted line). The rectangle has width r and height y. You plan to use 20 feet of framing. The cost of framing for the straight edges is $2 per foot. The cost of framing for the circular edge is $5 per foot. Write the constraint equation and the objective function for the optimiza- tion problem of finding the minimum cost, using the variables r and which is the objective and which is the constraint. You do not meed to find the minimum cost. y. Mark Reminder: A full circle of radius r has circumference 27r. The radius of a circle is 1/2 of the diameter. You should show some work for this problem.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Systems Of Equations And Inequalities
Section6.6: Linear Programming
Problem 50E
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5. You are framing a door, in the shape of a rectangle with a semicircle on top (see picture; there is no framing along the dotted line). The rectangle has width r and height y. You plan to use 20 feet of framing. The cost of framing for the straight edges is $2 per foot. The cost of framing for the circular edge is $5 per foot. Write the constraint equation and the objective function for the optimiza- tion problem of finding the minimum cost, using the variables r and y. Mark which is the objective and which is the constraint. You do not need to find the minimum cost. Reminder: A full circle of radius r has circumference 2nr. The radius of a circle is 1/2 of the diameter. You should show some work for this problem.
Transcribed Image Text:5. You are framing a door, in the shape of a rectangle with a semicircle on top (see picture; there is no framing along the dotted line). The rectangle has width r and height y. You plan to use 20 feet of framing. The cost of framing for the straight edges is $2 per foot. The cost of framing for the circular edge is $5 per foot. Write the constraint equation and the objective function for the optimiza- tion problem of finding the minimum cost, using the variables r and y. Mark which is the objective and which is the constraint. You do not need to find the minimum cost. Reminder: A full circle of radius r has circumference 2nr. The radius of a circle is 1/2 of the diameter. You should show some work for this problem.
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