Ask question

# For a certain product, the revenue is given by R = 40: and the cost is given by C = 20x + 1600. To obtain a profit, the revenue must be greater than the cost. For what values of x will there be a profit?

Question
Functions
asked 2020-11-08
For a certain product, the revenue is given by R = 40: and the cost is given by C = 20x + 1600. To obtain a profit, the revenue must be greater than the cost. For what values of x will there be a profit?

## Answers (1)

2020-11-09
The revenue must be greater than the cost so we write:
R>C
Substitute given functions:
40x>20x+1600
Subtract 20x from both sides:
20x>1600
Divide both sides by 20:
x>80
There will be a profit for x values greater than 80.

### Relevant Questions

asked 2021-01-05
A concert promoter produces two kinds of souvenir shirt, one kind sells for $18 ad the other for$25. The company determines, the total cost, in thousands of dollars, of producting x thousand of the $18 shirt and y thousand of the$25 shirt is given by
$$\displaystyle{C}{\left({x},{y}\right)}={4}{x}^{{2}}-{6}{x}{y}+{3}{y}^{{2}}+{20}{x}+{19}{y}-{12}.$$
How many of each type of shirt must be produced and sold in order to maximize profit?
asked 2021-01-19
A company that makes thing-a-ma-bobs has a start up cost of $44055. It costs the company$1.97 to make each thing-a-ma-bob. The company charges $5.31 for each thing-a-ma-bob. Let x denote the number of thing-a-ma-bobs produced. Write the cost function for this company. C(x) = Write the revenue function for this company. R(x) = What is the minumum number of thing-a-ma-bobs that the company must produce and sell to make a profit? asked 2020-12-30 A company produces two products A and B, which have profits of$9 and $7. Each unit of product must be processed on two assembly lines where the required production times are a follows: $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\left|{c}\right|}\right\rbrace}{h}{l}\in{e}\text{Product}&\text{Line 1}&\text{Line 2}\backslash{h}{l}\in{e}{A}&{12}&{4}\backslash{h}{l}\in{e}\text{Total hours}&{60}&{40}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ a. formulate a linear programming model to determine the optimal product mix that will maximize profit. b. transform this model into standard form. c. identify the amount of unused resources(i.e., slack)at each of the graphical extreme points. d. what would be the effect on the optimal if the production time on line 1 were reduced to 40 hours. c. What would be the effect on the optimal solution if the profit for product B were increased from$7 to $15? To$20?
asked 2020-10-23
The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P $$(A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).$$
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.
asked 2021-02-11
Several models have been proposed to explain the diversification of life during geological periods. According to Benton (1997), The diversification of marine families in the past 600 million years (Myr) appears to have followed two or three logistic curves, with equilibrium levels that lasted for up to 200 Myr. In contrast, continental organisms clearly show an exponential pattern of diversification, and although it is not clear whether the empirical diversification patterns are real or are artifacts of a poor fossil record, the latter explanation seems unlikely. In this problem, we will investigate three models fordiversification. They are analogous to models for populationgrowth, however, the quantities involved have a differentinterpretation. We denote by N(t) the diversification function,which counts the number of taxa as a function of time, and by rthe intrinsic rate of diversification.
(a) (Exponential Model) This model is described by $$\displaystyle{\frac{{{d}{N}}}{{{\left.{d}{t}\right.}}}}={r}_{{{e}}}{N}\ {\left({8.86}\right)}.$$ Solve (8.86) with the initial condition N(0) at time 0, and show that $$\displaystyle{r}_{{{e}}}$$ can be estimated from $$\displaystyle{r}_{{{e}}}={\frac{{{1}}}{{{t}}}}\ {\ln{\ }}{\left[{\frac{{{N}{\left({t}\right)}}}{{{N}{\left({0}\right)}}}}\right]}\ {\left({8.87}\right)}$$
(b) (Logistic Growth) This model is described by $$\displaystyle{\frac{{{d}{N}}}{{{\left.{d}{t}\right.}}}}={r}_{{{l}}}{N}\ {\left({1}\ -\ {\frac{{{N}}}{{{K}}}}\right)}\ {\left({8.88}\right)}$$ where K is the equilibrium value. Solve (8.88) with the initial condition N(0) at time 0, and show that $$\displaystyle{r}_{{{l}}}$$ can be estimated from $$\displaystyle{r}_{{{l}}}={\frac{{{1}}}{{{t}}}}\ {\ln{\ }}{\left[{\frac{{{K}\ -\ {N}{\left({0}\right)}}}{{{N}{\left({0}\right)}}}}\right]}\ +\ {\frac{{{1}}}{{{t}}}}\ {\ln{\ }}{\left[{\frac{{{N}{\left({t}\right)}}}{{{K}\ -\ {N}{\left({t}\right)}}}}\right]}\ {\left({8.89}\right)}$$ for $$\displaystyle{N}{\left({t}\right)}\ {<}\ {K}.$$
(c) Assume that $$\displaystyle{N}{\left({0}\right)}={1}$$ and $$\displaystyle{N}{\left({10}\right)}={1000}.$$ Estimate $$\displaystyle{r}_{{{e}}}$$ and $$\displaystyle{r}_{{{l}}}$$ for both $$\displaystyle{K}={1001}$$ and $$\displaystyle{K}={10000}.$$
(d) Use your answer in (c) to explain the following quote from Stanley (1979): There must be a general tendency for calculated values of $$\displaystyle{\left[{r}\right]}$$ to represent underestimates of exponential rates,because some radiation will have followed distinctly sigmoid paths during the interval evaluated.
(e) Explain why the exponential model is a good approximation to the logistic model when $$\displaystyle\frac{{N}}{{K}}$$ is small compared with 1.
asked 2021-03-05
Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold.
$$\begin{array}{|c|c|} \hline Number\ N & Price\ p\\ \hline 200 & 53.00\\ \hline 250 & 52.50\\\hline 300 & 52.00\\ \hline 350 & 51.50\\ \hline \end{array}$$
(a) Find a formula for p in terms of N modeling the data in the table.
$$\displaystyle{p}=$$
(b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month.
$$\displaystyle{R}=$$
Is R a linear function of N?
(c) On the basis of the tables in this exercise and using cost, $$\displaystyle{C}={35}{N}+{900}$$, use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month.
$$\displaystyle{P}=$$
(d) Is P a linear function of N?
asked 2021-03-11
Let's say the widget maker has developed the following table that shows the highest dollar price p. widget where you can sell N widgets. Number N Price p $$200 53.00$$
$$250 52.50$$
$$300 52.00$$
$$35051.50$$ (a) Find a formula for pin terms of N modeling the data in the table. (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in month as a function of the number N of widgets produced in a month. $$R=$$ Is Ra linear function of N? (c) On the basis of the tables in this exercise and using cost, $$C= 35N + 900$$, use a formula to express the monthly profit P, in dollars, of this manufacturer asa function of the number of widgets produced in a month $$p=$$ (d) Is Pa linear function of N2 e. Explain how you would find breakeven. What does breakeven represent?
asked 2021-03-05
1. A curve is given by the following parametric equations. x = 20 cost, y = 10 sint. The parametric equations are used to represent the location of a car going around the racetrack. a) What is the cartesian equation that represents the race track the car is traveling on? b) What parametric equations would we use to make the car go 3 times faster on the same track? c) What parametric equations would we use to make the car go half as fast on the same track? d) What parametric equations and restrictions on t would we use to make the car go clockwise (reverse direction) and only half-way around on an interval of [0, 2?]? e) Convert the cartesian equation you found in part “a” into a polar equation? Plug it into Desmos to check your work. You must solve for “r”, so “r = ?”
asked 2021-02-06
A.Which figure shows the loop that the must beused as the Ampèrean loop for finding for inside the solenoid?
B.Find , the z component of the magnetic field insidethe solenoid where Ampère's law applies. Express your answer in terms of,,,,and physical constants such as .
C.The magnetic field inside a solenoidcan be found exactly using Ampère's law only if thesolenoid is infinitely long. Otherwise, the Biot-Savart law must beused to find an exact answer. In practice, the field can bedetermined with very little error by using Ampère's law, aslong as certain conditions hold that make the field similar to thatin an infinitely long solenoid. Which of the following conditions musthold to allow you to use Ampère's law to find a goodapproximation?
Consider only locations where the distance from the ends ismany times . Consider any location inside the solenoid, as long asis much larger than for the solenoid. Consider only locations along the axis of the solenoid. Answer?
Show transcribed image text A. Which figure shows the loop that the must beused as the Amp?rean loop for finding B_z(r) for r inside the solenoid? B. Find B_z(r), the z component of the magnetic field insidethe solenoid where Amp?re's law applies. Express your answer in terms ofL,D,n,I,and physical constants such as mu_0. C. The magnetic field inside a solenoidcan be found exactly using Amp?re's law only if thesolenoid is infinitely long. Otherwise, the Biot - Savart law must beused to find an exact answer. In practice, the field can bedetermined with very little error by using Amp?re's law, aslong as certain conditions hold that make the field similar to thatin an infinitely long solenoid. Which of the following conditions musthold to allow you to use Amp?re's law to find a goodapproximation? Consider only locations where the distance from the ends ismany times D. Consider any location inside the solenoid, as long asLis much larger than Dfor the solenoid. Consider only locations along the axis of the solenoid.
asked 2020-11-10
When an electric current passes through two resistors with a resistance r1 and r2. connected in parallel, the combined resistance, R, can be calculated from the equation:
$$\frac{1}{R}=\frac{1}{2r1}+\frac{1}{3r2}$$
where R, r1 & r2 are greater than 0. Assume that r2 is constant. Show that RR is an increasing function of r1.
...