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15 Points!

The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 10 + 0.002p^3 and that its demand function is D(p) = 50 - 0.04p^2, where p is the price. Determine the price for which the supply equals the demand.

A) $21.86
B) $22.86
C) $21.36
D) $22.36

Respuesta :

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[tex]S(p)=D(p)\to10+0.002p^3=50-0.04p^2\\\\0.002p^3+0.04p^2-40=0\ \ \ |\cdot1000\\\\2p^3+40p^2-40000=0\ \ \ \ |:2\\\\p^3+20p^2-20000=0\to p\approx21.86[/tex]

Answer: A) $21.86

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