A) Demand function

price (x)          demand (D(x))

4                      540

3.50                  810

D - 540          810 - 540
----------- = -----------------
x - 4               3.50 - 4

D - 540
----------- = - 540
x - 4

D - 540 = - 540(x - 4)

D = -540x + 2160 + 540

D = 2700 - 540x

D(x) = 2700 - 540x

Revenue function, R(x)

R(x) = price * demand = x * D(x)

R(x) = x* (2700 - 540x) = 2700x - 540x^2

b) Profit, P(x)

profit = revenue - cost

P(x) = R(x) - 30

P(x) = [2700x - 540x^2] - 30

P(x) = 2700x - 540x^2 - 30

Largest possible profit => vertex of the parabola

vertex of 2700x - 540x^2 - 30

When you calculate the vertex you find x = 5 /2

=> P(x) = 3345

Answer: you should charge a log-on fee of $2.5 to have the largest profit, which is $3345.

5 0

3 years ago

Kathy’s customer base is 2/3 residential and 1/3 business if she has 350 residential customers how many total customers does she

Scorpion4ik [409]

If we made it into a ratio of residential customers to business customers, it would be a 2:1

350/2 = 175

350 + 175 = 525

525 total customers

4 0

3 years ago

The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standar

Serggg [28]

Answer:

The 95% confidence interval is given by:

3.30<σ<8.76

Step-by-step explanation:

1) Data given and notation

s=4.798 represent the sample standard deviation

$\bar x$ represent the sample mean

n=10 the sample size

Confidence=95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical values.

The excel commands would be: "=CHISQ.INV(0.025,9)" "=CHISQ.INV(0.975,9)". so for this case the critical values are:

$\chi^2_{\alpha/2}=19.022$

$\chi^2_{1- \alpha/2}=2.700$

And replacing into the formula for the interval we got:

$\frac{(9)(4.798)^2}{19.022} \leq \sigma \frac{(9)(4.798)^2}{2.700}$

$10.892 \leq \sigma^2 \leq 76.736$

Now we just take square root on both sides of the interval and we got:

$3.30 \leq \sigma \leq 8.76$

So the best option would be:

3.30<σ<8.76

7 0

3 years ago

Calculate had a net income of 5 million dollars in 2010, while a small competing company, Computate, had a

Julli [10]

9514 1404 393

Answer:

a) see the attached spreadsheet (table)

b) Calculate, for a 10-year horizon; Computate for a longer horizon.

c) Year 13; no

Step-by-step explanation:

a) The attached table shows net income projections for the two companies. Calculate's increases by 0.5 million each year; Computate's increases by 15% each year. The result is rounded to the nearest dollar.

b) After year 4, Computate's net income is increasing by more than 0.5 million per year, so its growth is faster and getting faster yet. However, in the first 10 years, Calculate's net income remains higher than that of Computate. If we presume that some percentage of net income is returned to investors, then Calculate may provide a better return on investment.

The scenario given here is only interested in the first 10 years. However, beyond that time frame (see part C), we find that Computate's income growth far exceeds that of Calculate.

c) Extending the table through year 13, we see that Computate's net income exceeds Calculate's in that year. It continues to remain higher as long as the model remains valid.

6 0

3 years ago