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UNO [17]
3 years ago
15

A manufacturer has a monthly fixed cost of $110,000 and a production cost of $14 for each unit produced. The product sells for $

20 per unit.
(a) What is the cost function?

C(x) =

(b) What is the revenue function?

R(x) =

(c) What is the profit function?

P(x) =

(d) Compute the profit or loss corresponding to a production level of 12,000 and 23,000 units. (Input a negative value to indicate a loss.)

at 12,000 units $ ______

at 23,000 units $______
Mathematics
1 answer:
vova2212 [387]3 years ago
5 0

Answer:

Cost function C(x) == FC + VC*Q

Revenue function R(x) = Px * Q

Profit function P(x) =(Px * Q)-(FC + VC*Q)

P(12000) = -38000 Loss

P(23000) = 28000 profit

Step-by-step explanation:

Total Cost is Fixed cost plus Variable cost multiplied by the produce quantity.  

(a)Cost function

C(x) = FC + vc*Q

Where  

FC=Fixed cost

VC=Variable cost

Q=produce quantity

(b)

Revenue function

R(x) = Px * Q

Where  

Px= Sales Price

Q=produce quantity

(c) Profit function

Profit = Revenue- Total cost

P(x) =(Px * Q)-(FC + vc*Q)

(d) We have to replace in the profit function

<u>at 12,000 units </u>

P(12000) =($20 * 12,000)-($110,000 + $14*12,000)

P(12000) = -38000

<u>at 23,000 units </u>

P(x) =($20 * 23,000)-($110,000 + $14*23,000)

P(23000) = 28000

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You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the
Vesna [10]

Answer:

A sample size of at least 1,353,733 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of .

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

98% confidence level

So \alpha = 0.02, z is the value of Z that has a pvalue of 1 - \frac{0.02}{2} = 0.99, so Z = 2.327.  

You would like to be 98% confident that you esimate is within 0.1% of the true population proportion. How large of a sample size is required?

We need a sample size of at least n.

n is found when M = 0.001.

Since we don't have an estimate for the proportion, we use the worst case scenario, that is \pi = 0.5

So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.001 = 2.327\sqrt{\frac{0.5*0.5}{n}}

0.001\sqrt{n} = 2.327*0.5

\sqrt{n} = \frac{2.327*0.5}{0.001}

(\sqrt{n})^{2} = (\frac{2.327*0.5}{0.001})^{2}

n = 1353732.25

Rounding up

A sample size of at least 1,353,733 is required.

5 0
3 years ago
2. A certain TV can be purchased from the manufacturer for $160. A certain online retailer has a standard markup of 30%, and a c
Vanyuwa [196]
Price, when purchased online:  1.30($160)
Price, when purchased at superstore:  1.40($160)

Difference in prices:  1.40($160) - 1.30($160) = 0.10($160) = $16

A higher markup brings a higher retail price.
8 0
3 years ago
The following function represents the value of a car, in dollars, after x years:
Assoli18 [71]

Answer:

Option D.The decrease in the value of the car, which is 8%

Step-by-step explanation:

we have a exponential function of the form

f(x)=a(b)^{x}

where

y is the value of the car

x is the time in years

a is the initial value

b is the base

r is the rate of decrease

b=1+r

In this problem we have

a=$24,000 initial value of the car

b=0.92

so

0.92=1+r

r=0.92-1=-0.08=-8%-----> is negative because is a rate of decrease

8 0
3 years ago
Read 2 more answers
Mrs.Hernandez told her class that 95% of the students in the class passed the math test if there are 20 students in the class ho
disa [49]

Answer:

19 people passed

Step-by-step explanation:

19 people passed the test

6 0
3 years ago
A phone company charges $0.06 per minute for local calls and $0.15 per minute for international calls. When your bill comes, it
solmaris [256]
Let's assume two variables x and y which represent the local and international calls respectively. 

x + y = 852 = total number of minutes which were consumed by the company (equation 1)
0.06*x+ 0.15 y =69.84 = total price which was charged for the phone calls (Equation 2)
 from equation 1:-
x=852 -y (sub in equation 2)
0.06 (852 - y) + 0.15 y =69.84

51.12 -0.06 y +0.15 y =69.84 (subtracting both sides by 51.12)
0.09 y =18.74
y= 208 minutes = international minutes (sub in 1) 
208+x=852 (By subtracting both sides by 208)
x = 852-208 = 644 minutes = local minutes
6 0
3 years ago
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