the four-step process to find R'(x). the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. nd to one decimal place as needed.)
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- The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x) = 56x – 0.020x? 0sxs 2800 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (Round to one decimal place as needed.) (B) R'(X) = (C) R(1000) = R'(1000) = Interpret these results. Choose the correct answer below. O A. This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is decreasing at a rate of R'(1000) dollars per seat. O B. This means that at a production level of 1,000 car seats, the revenue is R'(1000) dollars and is increasing at a rate of R(1000) dollars per seat. O c. This means that at a…What are the values of the function f(-2) f(3)Find the maximum of the function f defined as f(x) = 4x - 2x2 - 110 A
- Let Var(X) = 25 and Z= 2X + 5 Compute Var (Z)Find f'(x) for the given function. 9x f(x) = -X_ X- 1 f'(x) =A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from 250 units is $895. What is the average rate of change of the profit for this product when between 150 and 250 units are sold? Write the equation of the profit function for this product How many units give break-even for this product?
- Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is R(x) = 42x − 0.05x2. (a) Find R(50). $ Tell what it represents. 50 units produce this amount of revenue. The revenue decreases by about this amount when the number of units is increased from 50 to 51. The actual revenue of the 50th unit is this amount. 51 units produce this amount of revenue. The revenue increases by about this amount when the number of units is increased from 50 to 51. (b) Find the marginal revenue function. MR = (c) Find the marginal revenue (in dollars per unit) at x = 50. $ per unit Tell what it predicts about the sale of the next unit and the next 2 units. The sale of the next unit will the revenue by about $ . The sale of the next 2 units will the revenue by about $ . (d) Find R(51) − R(50). $ Explain what this value represents. actual revenue from the 50th unit actual revenue from 51 units…If Qd= 20-0.5P, find the slope of the function ?Can you help me find C(x) ?
- A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $5, and the society sells an average of 24 per week at a price of $9 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 3 sales per week. (a) Find a function that models weekly profit in terms of price per feeder. (Let x represent the price per feeder and P represent the profit.) P(x) = (b) What price should the society charge for each feeder to maximize profits? $ What is the maximum weekly profit? $y = (3 - x)6 + 7 apply the function in economic optimization conceptFind the limit of the function. Show your calculation.