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A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $10 per linear foot to install and the farmer is not willing to spend more than $5000, find the dimensions for the plot that would enclose the most area. (width, length
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $10 per linear foot to install and the farmer is not willing to spend more than $5000, find the dimensions for the plot that would enclose the most area. (width, length
width : 166.67 ft, length : 250 ftFurther explanationQuadratic function is a function that has the term x²The quadratic function forms a parabolic curveThe general formula isf (x) = ax² + bx + cwhere a, b, and c are real numbers and a ≠ 0.The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum valueSo the maximum is if a <0 and the minimum if a> 0.The formula for finding the coordinates of the maximum and minimum points of the quadratic function is the same.The maximum / minimum point of the quadratic function isWhereD = b²-4acTotal length of fence :x + 2yBecause the west side of the plot is shared with a neighbor, the equation becomes:x + 1.5ythe fencing costs $ 10 per linear foot, and the farmer is not willing to spend more than $ 5000, then the equation becomes:10x + 15y = 5000x + 1.5y = 500 ---> x = 500-1.5yThe area of the square :A = x.yWe input the value xA = (500-1.5y) yA = 500y-1.5y²The maximum area of the quadratic function is (a <0 means the maximum value)From the Area equation :a = -1.5, b = 500, c = 0D = b²-4acD = 500²-4.-1.5.0D = 500²D = 250,000Then the maximum area:value of xvalue of yy = A: xy = 41,666.6: 166.67y = 250 ftLearn moredomain of the functionbrainly.com/question/4135536the inverse of the ƒunctionbrainly.com/question/9289171F (x) = x2 + 1 g (x) = 5 - xhtps://brainly.com/question/2723982...