I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. I have a budget of $96 for the project. What are the dimensions of the vegetable patch with the largest area i can enclose?.
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The dimensions of the vegetable patch with the largest area we can enclose arelength = 12 feet and breadth = 6 feet.Given, a rectangular vegetable patch.The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot.We have a budget of $96 for the project.Let the length of the rectangle be, land breadth of the rectangle be, baccording to the ques,4l + 8b = 96l + 2b = 24l = 24 – 2bNow, area of the rectangle be,Area = length×breadthArea = l×bA = (24 – 2b)bA = 24b – 2b²On differentiating both sides, we getA’ = 24 – 4bb = 6l = 24 – 12 = 12So, the dimensions of the vegetable patch with the largest area we can enclose arelength = 12 feet and breadth = 6 feet.Hence, The dimensions of the vegetable patch with the largest area we can enclose arelength = 12 feet and breadth = 6 feet.Learn more about Application of Derivatives here https://brainly.com/question/25120629#SPJ4