Answer:
Dimensions are 350/9 ft and 17.5 ft
Step-by-step explanation:
We are given the cost per ft of all the 4 sides. Let the horizontal be x and the vertical be y.
Now, we will set up the constraint and equation that we are being asked to maximize.
Thus;
700 = 10y + 10y + 7x + 2x
700 = 20y + 9x
Maiking y the subject, we have;
y = (700 - 9x)/20
y = 35 - 9x/20
Now,area of a rectangle is: A = xy
Thus, A = x(35 - 9x/20))
A = 35x - 9x²/20
We can get the critical points by finding the derivatives and Equating to zero
Thus;
dA/dx = 35 - 0.9x
At dA/dx = 0,we have; x = 350/9
At d²A/dx², we have;
d²A/dx² = -0.9
This is negative, thus we will disregard and use the one gotten from the first derivative.
Thus, we will use x = 350/9 ft
Plugging this into the equation y = 35 - 9x/20, we have;
y = 35 - ((9 × 350/9)/20)
y = 17.5 ft
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