Answer :
The maximum revenue is $4,000 and 100 units should be manufactured to obtain the maximum revenue.
How to calculate a maximum of a function?
The maximums of a function are detected when the derivative becomes null and changes its sign (passing through 0 from the positive side to the negative side).
According to the given question:
Given function is
r(x) = 80x - 0.4x²
where the revenue r(x) is in dollar and no. unit is x.
We know that if function
y = ax²+bx+c.
Then we get the maximum value of y when x = -b/2a
Here a= -0.4 , b = 80 and c = 0.
Therefore,
x = -80/(2*-0.4)
x = 100
Therefore we get maximum revenue when x = 100.
∴ r(100) = 80.100- 0.4(100)²
=$4000
Therefore the maximum revenue is $4,000 and 100 units should be manufactured to obtain the maximum revenue.
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