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) (Show Source): You can put this solution on YOUR website!
Solving for Q in the given function, we get
a. For P = 169.50,
to the nearest whole number.
b.For P = 125.50,
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:
.
The algebra involved in solving for Q in terms of P would have taken into account the presence of 8 in the denominator.)
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