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olga55 [171]
1 year ago
10

A company is considering two different prize policies for a sweepstakes. In Policy A, the cost to enter is $5. and the overall w

in rate is 10%. 90% of the winners receive a product worth $10. 9.5% of the winners receive a product worth $50, and 0.5% of the winners receive $250 in cash. In Policy B, the cost to enter is $10, and the overall win rate is 15%, 80% of the winners receive a product worth $10, 18% of the winners receive a product worth $50, and 2% of the winners receive $250 in cash.
The company predicts that Policy A will attract 10.000 entries, and Policy B will attract 5000 entries. Which policy makes the largest proſt for the company? By how much?
a. Policy A, by 1500
b. Policy A, by 4000
c. Policy B, by 1500
d. Policy B, by 4000

An explanation would be really awesome!​
Mathematics
1 answer:
Natali5045456 [20]1 year ago
3 0

The policy that makes the largest proſit for the company is Policy A, by $1500.

<h3>Which policy makes the largest proſIt?</h3>

Profit is the amount paid by people to enter the sweepstakes less the amount they can win.

  • Policy A's profit: $5 - 0.1[(0.9 x $10) + (0.095 x $50) + (0.005 x $250)] = $5 - 1.5 = $3.5

$3.5 X 10,000 = $35,000

  • Policy B's profit:10 - 0.15[(0.8 x 10) + (0.18 x 50) + (0.02 x 250) = 10 - 3.30 = 6.7

$6.7 X 5000 = $33500

  • Difference in profits = $35,000 - 33500 = $1500

To learn more about profit, please check: brainly.com/question/26181966

#SPJ1

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Find the directional derivative of the function at the given point in the direction of the vector v. G(r, s) = tan−1(rs), (1, 3)
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The <em>directional</em> derivative of f at the given point in the direction indicated is \frac{5}{2}.

<h3>How to calculate the directional derivative of a multivariate function</h3>

The <em>directional</em> derivative is represented by the following formula:

\nabla_{\vec v} f = \nabla f (r_{o}, s_{o})\cdot \vec v   (1)

Where:

  • \nabla f (r_{o}, s_{o}) - Gradient evaluated at the point (r_{o}, s_{o}).
  • \vec v - Directional vector.

The gradient of f is calculated below:

\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{\partial f}{\partial r}(r_{o},s_{o})  \\\frac{\partial f}{\partial s}(r_{o},s_{o}) \end{array}\right]   (2)

Where \frac{\partial f}{\partial r} and \frac{\partial f}{\partial s} are the <em>partial</em> derivatives with respect to r and s, respectively.

If we know that (r_{o}, s_{o}) = (1, 3), then the gradient is:

\nabla f(r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{s}{1+r^{2}\cdot s^{2}} \\\frac{r}{1+r^{2}\cdot s^{2}}\end{array}\right]

\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{1+1^{2}\cdot 3^{2}} \\\frac{1}{1+1^{2}\cdot 3^{2}} \end{array}\right]

\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right]

If we know that \vec v = 5\,\hat{i} + 10\,\hat{j}, then the directional derivative is:

\nabla_{\vec v} f = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right] \cdot \left[\begin{array}{cc}5\\10\end{array}\right]

\nabla _{\vec v} f (r_{o}, s_{o}) = \frac{5}{2}

The <em>directional</em> derivative of f at the given point in the direction indicated is \frac{5}{2}. \blacksquare

To learn more on directional derivative, we kindly invite to check this verified question: brainly.com/question/9964491

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