Question

help please 31 and 32 .. i dont understand it

http://assets.openstudy.com/updates/attachments/574bc29be4b0d8d8e8043f2d-marcelie-1464582903284-math180final.pdf

Answer 1

For 32, you can write functions for the area and perimeter.
\(A = xy\)
\(P = 4x + 2y\)
But they also say that area is 10000 ft², so you can say \(xy = 10,000\)
Substitute for either x or y to make the perimeter a function of one variable
\[P=4x+\frac{20,000}{x}\]
Now take the derivative to find the values of x that minimize P

Answer 2

for 32,
Revenue = Quantity * Demand, so \(R(x)=x(90-x)\)
You're given the cost function, so the Profit function is
\(P(x) = R(x) - C(x)\)
\(P(x) = x(90-x)-(100+30x)\)
Again, take derivatives to find the x that maximized P(x)