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snow_lady [41]
4 years ago
8

A winery is supplied with crushed grapes once a week. If its weekly volume of sales in thousands of gallons is a random variable

with probability density function f (t) = {5 (1 -t)^4 0 < t < 1 0 otherwise what must the capacity of the tank be so that the probability of the supply being exhausted in a given week is 0.01?

Mathematics
1 answer:
alex41 [277]4 years ago
4 0

Answer:

<u><em>note:</em></u>

<u><em>solution is attached due to error in mathematical equation. please find the attachment</em></u>

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A company estimates that the revenue (in dollars) from the sale of x doghouses is given by R(x)=14,000ln(0.01x+1). Use the diffe
Dafna11 [192]

Answer:

The change in revenue from the sale of one more doghouse if 110 doghouses have already been sold is dR/dx=66.67 $/doghouse.

Step-by-step explanation:

We have a revenue function that is:

R(x)=14,000\cdot \text{ln}(0.01x+1)

We have to approximate the change in revenue from the sale of one more doghouse, if 110 doghouses have already been sold.

That is the marginal revenue at x=110.

The marginal revenue is expressed as the first derivative of the revenue.

Then, we calculate the derivative of R:

\dfrac{dR}{dx}=\dfrac{d}{dx}[14,000\cdot \text{ln}(0.01x+1)]\\\\\\\dfrac{dR}{dx}=14,000\dfrac{d}{dx}[\text{ln}(0.01x+1)]\\\\\\\dfrac{dR}{dx}=14,000\cdot\dfrac{1}{0.01x+1}\cdot \dfrac{d}{dx}(0.01x+1)\\\\\\\dfrac{dR}{dx}=14,000\cdot\dfrac{1}{0.01x+1}\cdot 0.01\\\\\\\dfrac{dR}{dx}=\dfrac{14,000}{x+100}

We then evaluate this marginal revenue at point x=110:

\dfrac{dR}{dx}_{|x=110}=\dfrac{14,000}{110+100}=\dfrac{14,000}{210}=66.67

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