Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

A farmer wants to fence in a rectangular plot in a large field, using a rock wall which is already there as the north boundary. The fencing for the east and west sides of the plot will cost $4 a yard, but the farmer needs to use special fencing which cost $5 a yard on the south side of a plot. If the area of the plot is to be 600 square yards, find the dimensions for the plot which will minimize the cost of the fencing.

Sagot :

caylus

Hello,

Let's assume x the length of the north's wall

and y the length of west side .

Area:x*y=600  ==> y=600/x

Cost: 2*y*4+5*x=8y+5x= 4800/x+5x

Minimize cost: (4800/x+5x)'=0

-4800/x²+5=0

x²=4800/5

x²=960

[tex]x=8\sqrt{15} \\\\y=5\sqrt{15} \\[/tex]

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.