Sally wants to build a three-sided fence enclosing a rectangular play area in her backyard. the area will be exactly 500 square feet. assume her house is wide enough that she will not need to use the entire length. the fence costs $5 per foot. find the length and width of the play area that minimize the cost of the fence. justify that you have found a minimum

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204