A page of 150 square inches is to have margins of 1 inch on either side and 1 1 2inches at the top and bottom, and the total area is 150 square inches, as in the diagram. Find the dimensions of the page (in inches) that maximize the print area.

Q: A rancher wants to create two rectangular pens, as shown in the figure, using an existing fence line…

A: The following solution is given below:

Q: You are assigned a task to design three rectangular cubicles lined up and sharing walls as in the…

A:

Q: A piece of wire 75m long and needs to be divided into two pieces. One piece will be used to form a…

A: Given data: The total length of the wire is L=75 m. The expression for the total length which is…

Q: Suppose a company's profits are given by P = x^2 y, where x is the amount of money they spend on TV…

A: given  P = x^2 y x+y=12

Q: A piece of wire 22 m long is cut into two pieces. One piece is bent into a square and the other is…

A:

Q: A rectangular area is to be enclosed and divided into thirds. The family has $640 to spend for the…

A: The calculation are as follows

Q: You want to build a 1100 square foot rectangular infinity pool. Three of the sides will have regular…

A:

Q: A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Let x m make a square.So each side= x/4 mArea of the square = (x/4)^2= x^2/16 m^2

Q: When a movie theater charges $12 for admission, there is an average attendance of 240 people per…

A: Given data;   The initial charge for a movie in a theater is x1=$12. The initial number of people…

Q: An open box is to be made from 72 square meters of cardboard, and the length of the box must be…

A:

Q: You want to build a 1000 square foot rectangular infinity pool. Three of the sides will have regular…

A:

Q: A rancher wants to build a rectangular corral for his horses. He also wants to split the corral into…

A:

Q: A wire 7 meters long is cut into two pieces. One piece is bent into a equilateral triangle for a…

A:

Q: An open box is to be made from a piece of cardboard, 15 inches by 15 inches, by cutting equal…

A:

Q: The area A of a triangle with two sides of equal length a is given by A = /P(P- a)²(P – b) where b…

A:

Q: A piece of wire 6 m long is cut into two pieces. One piece is bent into a square and the other is…

A:

Q: You are assigned a task to design three rectangular cubicles lined up and sharing walls as in the…

A: Let length of interior wall =x length of ourside wall=y total perimeter=270 4x+6y=270 2x+3y=135…

Q: rectangular lot is 12m long and 5m wide. The outside perimeter of the lot is to be provided with a…

A: Given that a rectangular lot is 12m long and 5m wide. The outside perimeter of the lot is to be…

Q: Your new puppy needs a rectangular dog run outside . You have 50 feet of fencing and plan to use the…

A: To maximize the area , we use Lagrange multipliers.

Q: A 100 ft stainless steel rope is to be cut into two sections. One of the sections will be used to…

A:

Q: A rectangular garden with an area of 500 yards is to be enclosed by a fence, and an additional fence…

A:

Q: You want to build a 1200 square foot rectangular infinity pool. Three of the sides will have regular…

A: Area of rectangular infinity pool is 1200 square foot. Cost of regular pool wall is $12 per foot,…

Q: You are assigned a task to design three rectangular cubicles lined up and sharing walls as in the…

A:

Q: An advertisement consists of a rectangular printed region plus 1-inch margins on the sides and…

A:

Q: In a world where people's happiness is the product of the square of the amount of one's food which…

A:

Q: A first class radio-telephone operator wishes to cut the wire 100 meters long into two pieces. One…

A:

Q: Bubba, a farmer, wants to fence-in a three-sided area next to his barn, using the side of the barn…

A:

Q: Albert wants to make an open box from a rectangular piece of cardboard by cutting squares out of the…

A: given ,  measure of cardboard , length =32 inches   and   breadth = 20 inches

Q: A rectangular poster is to contain 128 square inches of print. The margins at the top and bottom of…

A: Let the length of the rectangle be x Length after 1 inches of margin = x-2  inch The breadth of…

Q: An oil- producing country can sell 7 million barrels of oil a day at price of $90 per barrel. If…

A:

Q: The monthly output of a Spanish light bulb factory is P = 2LK2 (in millions), where L is the cost of…

A:

Q: At the Pizza Dude restaurant, a 12-in. pizza costs $5.40 to make, and the manager wants to make at…

A: Given: cost price of pizza=$5.40, profit earn by manager=$4.80 We know that selling priceS.P. of…

Q: How would you divide a 27 inch line into two parts of length A and B so that A+B=27 and the product…

A:

Q: A rectangle whose width is less than its length by 3 and its area is 4, then its length is

A: Please refer the attached image for complete solution.

Q: A track and field area is to be constructed in the shape of a rectangle with semicircles at each…

A: From the given data:

Q: A rectangular poster is to contain 648 square inches of paint. The margins at the top and bottom of…

A:

Q: An 6 in x 10 in sheet of paper is to be folded into a box, with one side open, by cutting squares in…

A:

Q: A car manufacturer estimated that the cost of production of “x” cars of a certain model is C = 20x –…

A:

Q: An apple grower finds that if she plants 70 trees per acre, each tree will yield 164 bushels of…

A:

Q: A rectangular poster is to contain 578 square inches of print. The margins at the top and bottom of…

A: Let the height of the poster = x inch  Let the breadth of the poster = y inch  Height of the print…

Q: A gardener has 60 yards of fencing and wants to enclose a rectangular garden that requires fencing…

A: GivenAmount of fence available=60 yards

Q: You have 200 feet of wire fencing, and you will only need to fence in three sides because the barn…

A: Let width=x and length= y  So, 2x+y=200 Or, y=200-2x

Q: You are assigned a task to design three rectangular cubicles lined up and sharing walls as in the…

A: Let, y b the length of the other side of the cubicles. So, the perimeter of the rectangular…

Q: You want to build a 1100 square foot rectangular infinity pool. Three of the sides will have regular…

A: Given problem:- You want to build a 1100 square foot rectangular infinity pool. Three of the sides…

Q: A rectangular poster is to contain 648 square inches of print. The margins at the top and bottom of…

A: Given: The area of the poster is 648 square inches. The following diagram shows all the…

Q: You have 800 feet of fencing to make a pen for hogs. If you have a river on one side of your…

A: We have to make a pen for hogs with 800 feet of fencing. There is a river on one side of the…

Q: A financier plans to invest up to $500,000 in two projects. Project A yields a return of 9% on the…

A: Total investment = x+y Given that the financier plans to invest up to $500,000 in two projects. So,…

Q: You are assigned a task to design three rectangular cubicles lined up and sharing walls as in the…

A: We can solve the given problem by using the second derivative test.

Q: Consider the following problem: a farmer with 750 feet of fencing wants to enclose a rectangular…

A: Solution Given A farmer with 750 feet fencing wants to enclosed  a rectangular area and then divide…