Calculus Help!! :)

Question

A farmer wants to fence in a rectangular field. The farmer must use a different type of fencing for each pair of parallel sides of the field. One type costs $10 per metre, and the other type costs $5 per metre. Assuming the farmer can spend $800 on fencing in total, what are the dimensions of the largest possible field she could make?

Answer 1

x = dimension of $10/metre fencing

y = dimension of $5/metre fencing

Total spending: 800 = 2x*10 + 2y*5 (2 sides each)

Solve that equation for y = ....

You want to maximize the field area: A(x) = x*y (substitute the expression for y that you found earlier so A is a function of x only).

A(x) will be a quadratic function. The maximum will be at the vertex. The x value for which the vertex occurs can be found with algebra x = -b/(2a) or using calculus A'(x) = 0 ....

After you find the x value of the maximum, use the formula for y that you found earlier to calculate the y dimension.