Complete the following applied optimization word problem. Include a well-labeled figure,clearly defined objective function of one variable, interval for which that variable is logical,and supporting mathematical statements to justify that the optimal result is achieved forthe function on the interval within a grammatically correct exposition.Suppose Hayley wants to mail a poster inside a cylindrical container. To mail a cylindricalpackage with UPS without additional fees, the sum of the length of the package and thegirth of the package must be less than or equal to 110 inches, where the girth is the circulardistance around the package. What is the largest volume that her package can have?

Given: Let the lenght of of the package= x the radius of of the package= r…

Suppose Hayley wants to mail a poster inside a cylindrical container. To mail a cylindrical package with UPS without additional fees, the sum of the length of the package and the girth of the package must be less than or equal to 110 inches, where the girth is the circular distance around the package. What is the largest volume that her package can have?

Suppose Hayley wants to mail a poster inside a cylindrical container. To mail a cylindrical package with UPS without additional fees, the sum of the length of the package and the girth of the package must be less than or equal to 110 inches, where the girth is the circular distance around the package. What is the largest volume that her package can have?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 39E

See similar textbooks

Similar questions

Complete the following applied optimization word problem. Include a well-labeled figure,clearly defined objective function of one variable, interval for which that variable is logical, and supporting mathematical statements to justify that the optimal result is achieved for the function on the interval within a grammatically correct exposition. Suppose Hayley wants to mail a poster inside a cylindrical container. To mail a cylindrical package with UPS without additional fees, the sum of the length of the package and the girth of the package must be less than or equal to 80 inches, where the girth is the circular distance around the package. What is the largest surface area that her package can have?
Complete the following applied optimization word problem. Include a well-labeled figure, clearly defined objective function of one variable, interval for which that variable is logical, and supporting mathematical statements to justify that the optimal result is achieved for the function on the interval within a grammatically correct exposition. Suppose Hayley wants to mail a poster inside a cylindrical container. To mail a cylindrical package with FedEx without additional fees, the sum of the length of the package and the girth of the package must be less than or equal to 80 inches, where the girth is the circular distance around the package. What is the largest volume that her package can have?
Complete the following applied optimization word problem. Include a well-labeled figure,clearly defined objective function of one variable, interval for which that variable is logical,and supporting mathematical statements to justify that the optimal result is achieved forthe function on the interval within a grammatically correct exposition. Suppose Hayley wants to mail a poster inside a cylindrical container. To mail a cylindricalpackage with UPS without additional fees, the sum of the length of the package and thegirth of the package must be less than or equal to 110 inches, where the girth is the circulardistance around the package. What is the largest volume that her package can have? I want WrittenJustifications please!
Complete the following applied optimization word problem. Include a well-labeled figure, clearly defined objective function of one variable, interval for which that variable is logical, and supporting mathematical statements to justify that the optimal result is achieved for the function on the interval within a grammatically correct exposition. To mail a package with the United States Postal service without additional fees, the sum of the length and the girth of the package must be less than or equal to 120 inches, where the length is the length of the longest side and the girth is the distance around the package perpendicular to its length. Suppose Torre wants to mail a box with a length of 60 inches.What is the largest possible volume that Torre’s package can have? Make sure that the length of the package corresponds to the longest side.
Complete the following applied optimization word problem. Include a well-labeled figure, clearly defined objective function of one variable, interval for which that variable is logical, and supporting mathematical statements to justify that the optimal result is achieved for the function on the interval within a grammatically correct exposition. A hiker is returning to a campsite that is 2 miles east and 5 miles north from their current position. The hiker is currently walking east along a path at a pace of 5 miles per hour. The hiker plans to leave the path and walk in a straight line, diagonally towards the cabin through the woods. The hiker can only walk at a pace of 2 miles per hour through the woods. Where should the hiker leave the path and turn into the woods if they want to get to the campsite as quickly as possible?
Complete the following applied optimization word problem. Include a well-labeled figure, clearly defined objective function of one variable, interval for which that variable is logical, and supporting mathematical statements to justify that the optimal result is achieved for the function on the interval within a grammatically correct exposition.A pipe must be buried underground to reach from a station on the shoreline to an outpost that is 6 miles down the shoreline and 2 miles into the ocean from the shoreline. It costs $5,000 per mile to bury the pipe under the ocean floor and $1,000 per mile bury the pipe along the shoreline. How far along the shore should the pipe be buried before turning towards the outpost if the goal is to minimize the cost?
Let L be the length of the ladder, x be the distance from the base of the ladder to the fence, d be the distance from the fence to the house and b be the distance from the ground to the point the ladder touches the house. What is the objective function, in terms of x? (type expression) What is the length of the shortest ladder?
Complete the following applied optimization word problem. Include awell-labeled figure, clearly defined objective function of one variable, interval for which thatvariable is logical, and supporting mathematical statements to justify that the optimal resultis achieved for the function on the interval within a grammatically correct exposition. A hiker is returning to a campsite that is 2 miles east and 5 miles north from their currentposition. The hiker is currently walking east along a path at a pace of 5 miles per hour. Thehiker plans to leave the path and walk in a straight line diagonally towards the cabin throughthe woods. The hiker can only walk at a pace of 2 miles per hour through the woods. Whereshould the hiker leave the path and turn into the woods if they want to get to the campsiteas quickly as possible?
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(p) = - 4p2 + 4000p What unit price should be established for the dryer to maximize revenue? What is the maximum revenue?
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(p)=-9p2+27,00p What unit price should be established for the dryer to maximize revenue? What is the maximum revenue?
Suppose that an appliance maker determines that in order to sell q appliances, the price per appli-ance must bep = 280 ? 0.4qThe appliance maker has also determined the total cost to produce q appliances isC(q) = 5000 + 0.6q2(a) What is the revenue function R(q)?(b) What is the prot function P(q)?(c) What is the maximum prot?(d) How many items must be produced and sold to yield the maximum prot?(e) What price per appliance must be charged to maximize prot?1
Write the Kuhn-Tucker conditions and find the maximum value of y=x-.25x^2+y^2 subject to .5x^2+y^2≤(less than or equal to)11/8, y≥0, x≥0 (both greater than or equal to 0) and test the shape of the objective function for a maximum or minimum. Must use Kuhn-Tucker Method.