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Answer:
Between 1000 and 5000 snowboards will make the function AP(x) >0.
Step-by-step explanation:
Since x can only take possitive values, we have that AP(x) = P(x)/x > 0 if and only if P(x) > 0.
In order to find when P(x) > 0, we find the values from where it is 0 and then we use the Bolzano Theorem.
P(x) = R(x) - C(x) = -x²+10x - (4x+5) = -x²+6x - 5. the roots of P can be found using the quadratic formula:
Therefore, P(1) = P(5) = 0. Lets find intermediate values to apply Bolzano Theorem:
- P(0) = -5 < 0 ( P is negative in (-∞ , 1) )
- P(2) = -4+6*2-5 = 3 > 0 (P is positive in (1,5) )
- P(6) = -36+36-5 = -5 < 0 (P is negative in (5, +∞) )
The production levels that make AP(x) >0 are between 1000 and 5000 snowboards (because we take x by thousands)