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2 years ago

10 POINTS!!! FULL ANSWER WITH FULL STEP BY STEP SOLUTION PLEASE

Mathematics

1 answer:

Inga [223]2 years ago

3 0

A) Profit is the difference between revenue an cost. The profit per widget is
m(x) = p(x) - c(x)
m(x) = 60x -3x^2 -(1800 - 183x)
m(x) = -3x^2 +243x -1800
Then the profit function for the company will be the excess of this per-widget profit multiplied by the number of widgets over the fixed costs.
P(x) = x×m(x) -50,000
P(x) = -3x^3 +243x^2 -1800x -50000

b) The marginal profit function is the derivative of the profit function.
P'(x) = -9x^2 +486x -1800

c) P'(40) = -9(40 -4)(40 -50) = 3240
Yes, more widgets should be built. The positive marginal profit indicates that building another widget will increase profit.

d) P'(50) = -9(50 -4)(50 -50) = 0
No, more widgets should not be built. The zero marginal profit indicates there is no profit to be made by building more widgets.

_____
On the face of it, this problem seems fairly straightforward, and the above "step-by-step" seems to give fairly reasonable answers. However, if you look at the function p(x), you find the "best price per widget" is negatve for more than 20 widgets. Similarly, the "cost per widget" is negative for more than 9.8 widgets. Thus, the only reason there is any profit at all for any number of widgets is that the negative costs are more negative than the negative revenue. This does not begin to model any real application of these ideas. It is yet another instance of failed math curriculum material.

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Please help me with this word problem!!!

Inessa [10]

Answer:

The number of customers needed to break even is

$\simeq 6775.$

Step-by-step explanation:

Rent per month = $ 7200

Rent per year, $ $7200 \times 12$

= $ 86400 -------------(1)

Insurance per year = $ 4200 ---------(2)

Total direct cost for 2 servers (withoout tax) per year,

= $ $2 \times 15 \times 8 \times 5 \times 50$

= $ 60000

Total cost for helper ( without tax) per year,

= $ $4 \times 15 \times 5 \times \50$

= $ 15000

Total cost for employees per year (without tax),

= $ (60000 +15000) = $ 75000

Total cost per year for employees including tax,

$ $\frac {(75000 \times (100 + 6.2 + 1.45)}{100}$

= $ $\frac {(75000 \times 107.65 }{100}$

= $ 80737.5 -----------------------(3)

So,

total cost for running the restaurant (except food)

= (1) + (2) + (3) = $ $(86400 + 4200 + 80737.5)$

= $ 171337.5

Average total profit per customer,

= ( Average per customer payment - average cost of food per customer)

= $ (45.47 - 20.18)

= $ 25.29

So, total number of customer needed to break even,

= $\frac {171337.5}{25.29}$

\simeq 6775

7 0

2 years ago

If f(x)=-x+2, find f(4)

pickupchik [31]

Answer:

f(4)=-2

Step-by-step explanation:

f(4)=-4+2=-2

5 0

2 years ago

Hannah claims that people who live in southern states spend 9 hours more per week outside than do people in northern states. She

vova2212 [387]

Answer:

b. Hannah is likely to be incorrect because 9 is not contained in the interval.

Step-by-step explanation:

Hello!

Hannah estimated per CI the difference between the average time that people spend outside in southern states and the average time people spend outside in northern states.

The CI is a method of estimation of population parameters that propose a range of possible values for them. The confidence level you use to construct the interval can be interpreted as, if you were to calculate 100 confidence interval, you'd expect that 99 of them will contain the true value of the parameter of interest.

In this example, the 99%CI resulted [0.4;8.0]hs

Meaning that with a 99% confidence level you'd expect the value of the difference between the average time people from southern states spend outside than the average time people from northern states spend outside is included in the interval [0.4;8.0]hs.

Now, she claims that people living in southern states spend 9 more hours outside than people living in northern states, symbolized μ₁ - μ₂ > 9

Keep in mind that if you were to test her claim, the resulting hypothesis test would be one-tailed

H₀: μ₁ - μ₂ ≤ 9

H₁: μ₁ - μ₂ > 9

And that the calculated Ci is tow-tailed, so it is not valid to use it to decide over the hypotheses pair. This said, considering that the calculated interval doesn't contain 9, it is most likely that Hannah's claim is incorrect.

I hope this helps!

6 0

2 years ago

A commuter must pass through 5 traffic lights on her way to work and will have to stop at each one that is red. She estimates th

sergij07 [2.7K]

Answer:

(a) The mean or expected value of X is 2.2.

(b) The standard deviation of X is 1.3.

Step-by-step explanation:

Let X = number of times the traffic light is red when a commuter passes through the traffic lights.

The probability distribution of X id provided.

The formula to compute the mean or expected value of X is: