You have decided to help your friend build pens for her farm animals. She has 8000 ft of fencing for the pens, and want to build four equally-sized pens with some shared sides (as shown in the diagram) as she needs to keep some of the animals separated. How should she build the pens to maximize the enclosed area? What is the maximum area?

Q: A farmer finds that if she plants 100 trees per acre, each tree will yield 45 bushels of fruit. She…

A: Here we will find the number of trees per acre to maximise harvest,

Q: A manufacturing company has the following cost and revenue functions: C(x) = 3600 + 25x +x² and R(x)…

A: Break-even point: It is the point at which the cost and revenue are same. Profit = Revenue - Cost.…

Q: The back of Dante's property is a creek. Dante would like to enclose a rectangular area, using the…

A: Given :- The back of Dante's property is a creek. Dante would like to enclose a rectangular area,…

Q: Suppose a baby food company has determined that its total revenue R for its food is given by R = 23…

A:

Q: The manager of a large apartment complex knows from experience that 80 units will be occupied if the…

A: The manager of a large apartment complex knows from experience that 80 units will be occupied if the…

Q: The manager of a large apartment complex knows from experience that 90 units will be occupied if the…

A: let R be the revenue, and let n be the number of (up or down) $4 in rent. Hence the equation for…

Q: Skippy wishes to plant a vegetable garden along one side of his house. In his garage, he found 28…

A: Given,Skippy found 28 linear feet of fencing and one side of garden need not fencing.We have to find…

Q: An apple grower finds that if he plants 80 trees per acre, each tree will yield 26 bushels of fruit.…

A:

Q: 2. A rancher from above needs two equal adjacent rectangular pens that share a fence in the middle.…

A: Given that ,Rancher needs two equal adjacent rectangular pens with a fence in middle. this can be as…

Q: In a grocery store, shelf space is limited and must be used effectively to increase profit. Two…

A:

Q: A pencil cup with a capacity of 36 square inches is to be constructed in the shape of a rectangular…

A: Use application of derivative to find dimensions of the cup to minimize construction cost.

Q: A rectangular box of height y having a square base with sidelength x is to be made. If the area of…

A:

Q: An apple grower finds that if she plants 60 trees per acre, each tree will yield 222 bushels of…

A: Let x be the additional number of trees planted on the 1 acre land. Let y be the total harvest of…

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

A:

Q: You are at a Halloween party and the hostess hands each guest a piece of square cardboard measuring…

A: Let the length of the side of each square cut off from the corners be x inch. Then, height of the…

Q: A company has $24000 to spend on the development and promotion of a new product. The company 5 1…

A: It is given that x dollars is spent on development and y dollars is spent on promotion Total amount…

Q: A page of 150 square inches is to have margins of 1 inch on either side and 1 1 2inches at the top…

A:

Q: A homeowner wants to build, along his driveway, a garden surrounded by a fence. If the garden is to…

A:

Q: If a consumer has an income of $200, the price of X is $5, and the price of Y is $10, what is the…

A: We will solve the following

Q: Define the livable space of a building to be the volume of space in the building where a person 6…

A:

Q: Use Lagrange multipliers to find the maximum production level when the total cost of labor (at $112…

A: The solution of the problem is given in the next steps.

Q: A farmer finds that if she plants 85 trees per acre, each tree will yield 65 bushels of fruit. She…

A: answer is in next step

Q: A boat on the ocean is 9 km from the nearest point on a straight shoreline; that point is 10 km from…

A:

Q: A farmer finds that if she plants 60 trees per acre, each tree will yield 35 bushels of fruit. She…

A:

Q: Afarmer finds that if she plants 100 trees per acre,, each tree will yield 40 bushels of fruit. She…

A:

Q: A visitor is staying in a cottage that is 10 miles east of the closest point on a shoreline to an…

A: Given A visitor is staying in a cottage that is 10 miles east of the closest point on a shoreline to…

Q: A merchant wants to create a rectangular display area in front of her store. The area is to be…

A:

Q: The manager of a 100 unit apartment complex is trying to decide what to charge for rent. Experience…

A:

Q: You have a wire of length 2 m, which you can bend either into a square or a circle. You also have…

A:

Q: The manufacturer of a CD player has found that the revenue R​ (in dollars) is R (p)=-5p2 + 1920p…

A:

Q: A farmer finds that if she plants 55 trees per acre, each tree will yield 50 bushels of fruit. She…

A: Let x be trees per acre and y be yield.  The given data is represented in an equation,…

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

A:

Q: A rancher has 240 ft of fencing with which to build a rectangular corral alongside an existing…

A:

Q: The CMO of ABC Company presumed that the demand for a Product Y can be modeled by p=80-0.01y where p…

A: Maximum profit will occur at that value of x when derivative of profit function is zero. We will…

Q: Bill is constructing a rectangular corral in his yard. He only has 32 ft of fencing material and…

A: Bill is constructing a rectangular corral in his yard and he has only 32 ft of fencing material. We…

Q: A company manufactures two types of athletic shoes: jogging shoes and cross-trainers. The total…

A: Rx(x,y)= -10x-2y+42 Ry(x,y) = -16y-2x+102

Q: Bob wants to create two pens, as shown in the figure. One pen is for a garden and it needs a heavy…

A:

Q: Professor Calderon wants to build a rectangular fence along a pond so his dogs can go for a swim; he…

A:

Q: A home gardener estimates that 19 apple trees will have an average yield of 147 apples per tree. But…

A: Total  number of apple  trees=x+19GIVEN:Additional tree planted the yield will decrease by three…

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

A: Here we use the second derivative test to find the dimensions of the required box.

Q: The school director of Saint Louis School of Pacdal, Inc, wants to construct a rectangulr wants to…

A: To find: The dimensions of the garden to be maximized: Given information: The school director wants…

Q: A small generator burns 2 types of fuel: low sulfur and high sulfur to produce electricity. For one…

A: Consider the provided question, Let x be the number of gallons of low sulfur and, y be the number of…

Q: An apple grower finds that if she plants 60 trees per acre, each tree will yield 350 bushels of…

A: If she plants 60 trees per acre then Yield per tree is 350 bushels Let additional no. Of trees she…

Q: A farmer finds that if she plants 70 trees per acre, each tree will yield 30 bushels of fruit. She…

A:

Q: Find the maximum profit and the number of units that must be produced and sold in order to achieve…

A: Given  R(x)=x2+110x+60C(x)=1.1x2+10x+80

Q: The manager of a large apartment complex knows from experience that 80 units will be occupied if the…

A: Let us assume he has to increase 3 dollars x times.So, the new rent= 396-3x Number of units will be…

Q: Isabel has up to P450 000 to invest in two types of investments. Type A investment pays 6% annually…

A: We are given a Portfolio optimization situation. We have the following facts in our hand  Isabel has…

Q: 3. Rae plans to build a rectangular pig pen against one of the walls of her barn. If she has 18…

A: