SOLUTION: The demand curve for a specially brewed Caribbean Rum is given by 𝑃 = 8000 (1 − (8 )/( e^(-0.001Q ) + 8 )), where P is the price per 750ml bottle and Q the numbe

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Question 1021550: The demand curve for a specially brewed Caribbean Rum is given by
𝑃 = 8000 (1 − (8 )/( e^(-0.001Q ) + 8 )), where P is the price per 750ml bottle and Q the number of bottles demanded.
a. Approximately how many bottles will be demanded when the price is $169.50?
b. Approximately how many more bottles will be demanded if the price fell to $125.50?
What price should a bottle sell for if only 1000 bottles were brewed and brewery wanted to satisfy the demand exactly?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Solving for Q in the given function, we get
ln%28%288P%29%2F%288000+-+P%29%29%2F-0.001+=+Q
a. For P = 169.50,
Q+=+ln%28%288%2A169.50%29%2F%288000+-+169.50%29%29%2F-0.001+=+1753 to the nearest whole number.
b.For P = 125.50,
Q+=+ln%28%288%2A125.50%29%2F%288000+-+125.50%29%29%2F-0.001+=+2060 to the nearest whole number.
==> 307 more bottles will be demanded if the price fell to $125.50.
c. Just substitute Q = 1000 into the expression for P and use your scientific calculator to evaluate. (The answer is $351.70.)
(The 8 in the denominator is not part of the exponent of e, so the equation looks like this:
+P=+8000+%281+-+8+%2F%28+e%5E%28-0.001Q%29+%2B+8%29%29.
The algebra involved in solving for Q in terms of P would have taken into account the presence of 8 in the denominator.)