Question

Great Green, Inc determines that it’s marginal revenue per day is given by: R’(t)= 75e^t-2t, R(0)=0,...

Great Green, Inc determines that it’s marginal revenue per day is given by:

R’(t)= 75e^t-2t, R(0)=0,

where R(t) is the total accumulated revenue, in dollars, on the t^th day. The company’s marginal cost per day is given by:

C’(t)=75-3t, C(0)=0,

where C(t) is the total accumulated cost in dollars on the t^th day.

a. find the total profit from t=0 to t=10

b. find the average daily profit for the first 10 days

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A company determines that its marginal revenue per day is given by R′(t)​, where R(t) is...
A company determines that its marginal revenue per day is given by R′(t)​, where R(t) is the total accumulated​ revenue, in​ \ dollars, on the tth day. The​ company's marginal cost per day is given by C′(t)​, where C(t) is the total accumulated​ cost, in​ dollars, on the tth day. R′(t)=130et​, R(0)=​0; C′(t)=130−0.8t​, C(0)=0 ​a) Find the total profit​ P(T) from t=0 to t=10 ​(the first 10 ​days). P(T)=R(T)−C(T)=∫T0R′(t)−C′(t) dt The total profit is $___ ​(Round to the nearest cent...
The marginal revenue of a company is given by r(x)=x^3-0.3x^2+0.1 and the marginal cost is given...
The marginal revenue of a company is given by r(x)=x^3-0.3x^2+0.1 and the marginal cost is given by c(x)=x\sqrt{-x^2+100} both measured in thousands of dollars per hundred units (x) produced. Find the total profit for x=1 to x=4 hundred units produced.
Given the revenue and cost functions R = 26x - 0.3x2 and C = 3x +...
Given the revenue and cost functions R = 26x - 0.3x2 and C = 3x + 10, where x is the daily production, find the rate of change of profit with respect to time when 20 units are produced and the rate of change of production is 7 units per day per day.
6. Given vector function r(t) = t2 − 2t, 1 + 3t, 1 3 t 3...
6. Given vector function r(t) = t2 − 2t, 1 + 3t, 1 3 t 3 + 1 2 t 2 i (a) Find r 0 (t) (b) Find the unit tangent vector to the space curve of r(t) at t = 3. (c) Find the vector equation of the tangent line to the curve at t = 3
Suppose the annual revenue of a startup can be modeled by the equation R(t) = (2t)/(t...
Suppose the annual revenue of a startup can be modeled by the equation R(t) = (2t)/(t + 3) million dollars where t is the number of years from now. A. At what rate will the annual revenue of the startup be increasing 2 years from now? Give an approximation rounded to two decimal places. B. What will be the total revenue of the startup over the next 5 years. Give an approximation rounded to two decimal places. FOR THE NEXT...
Suppose the annual revenue of a startup can be modeled by the equation R(t) = (2t)/(t...
Suppose the annual revenue of a startup can be modeled by the equation R(t) = (2t)/(t + 3) million dollars where t is the number of years from now. A. At what rate will the annual revenue of the startup be increasing 2 years from now? Give an approximation rounded to two decimal places. B. What will be the total revenue of the startup over the next 5 years. Give an approximation rounded to two decimal places. C. What will...
The revenue function of a company is given by R(x)=-2x^2+25x+150, the cost function is given by...
The revenue function of a company is given by R(x)=-2x^2+25x+150, the cost function is given by C(x)=13x+100 a. Find the marginal cost and marginal revenue function. b. Find the production level x where the profit is maximized. Then find the maximum profit.
The total revenue function for a certain product is given by R=590x dollars, and the total...
The total revenue function for a certain product is given by R=590x dollars, and the total cost function for this product is C=15,000 +50x + x squared 2 dollars, where x is the number of units of the product that are produced and sold. a. Find the profit function. b. Find the number of units that gives maximum profit. c. Find the maximum possible profit.
A company's revenue from selling x units of an item is given as R=1900x−2x^2. If sales...
A company's revenue from selling x units of an item is given as R=1900x−2x^2. If sales are increasing at the rate of 50 units per day, how rapidly is revenue increasing (in dollars per day) when 360 units have been sold? ? dollars per day The cost of producing x units of stuffed alligator toys is C(x)=0.002x^2+7x+5000. Find the marginal cost at the production level of 1000 units. ? dollars/unit Suppose a product's revenue function is given by R(q)=−7q^2+600q ,...
Consider the parameterized motion given by r(t)=3t^2i-2t^2j+(6-t^3)k. Where is the object at time t=1? What is...
Consider the parameterized motion given by r(t)=3t^2i-2t^2j+(6-t^3)k. Where is the object at time t=1? What is the velocity at t=1? What is the speed at t=1? How far does the object move from 0≤t≤1? Round your answer to 2 decimal places. * r, i, j, and k should all have vector arrows above them