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- Find f'(x) for the given function. 9x f(x) = -X_ X- 1 f'(x) =What are the values of the function f(-2) f(3)It costs a baker a fixed cost of $420 and variable cost of $2.10 per cupcake. A cupcake is sold for $4.90 each. (iv) Write an algebraic expression representing the revenue R as a function of the number of cupcakes x sold.(v) Graph both functions on the same coordinate axes.(vi) From your graph find coordinatae at which cost equals revenue.(vii) Using your graph, determine how many cupcakes need to be made to produce revenue of at least $1,029. How much profit is made for this number of cupcakes?
- It is estimated that a grocer’s daily profit from the sale of two brands of cherry juice is given by thefunction:P(x,y) = (x - 30)(70 - 5x + 4y) + (y – 40)(80 + 6x – 7y) centswhere x is the price per can of Brand V Juice and y is the price per can of Brand Triple V Juice. CurrentlyBrand V Juice sells for 50 cents per can and Brand Triple V Juice sells for 52 cents per can.i. Use marginal analysis to estimate the change in the daily profit that will result if the grocer raises theprice of Brand Triple V by one cent per can while keeping the price of Brand V unchanged.ii. Find a stationary point of the daily profit function. Classify this stationary point.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…Technology B uses 4 workers and 2 tonnes of coal to produce 100 meters of cloth. The worker's wages cost $10 and coal costs $5. We have previously calculated that the total cost of production is $50 and that the vertical intercept of the isocost line is 10.If there was a technology that used 1 more worker, how much would it have to decrease the coal required in order to cost the same? (Note: this is the absolute value of the slope of the isocost line.)
- Whenever postage rates change, some newspaper publishes a graph such as the one shown below, which shows the price of a first-class stamp from 2006 to 2016. Cost(dollam) 0.85- 0.70- 0.55 0.40 0.25 of 2006 2008 Price of a First-Class Stamp [Select] 2010 Year 2012 2014 2016 (a) Let f be the function whose rule is f(x) = cost of a first-class stamp in year x. Find f(2012) and f(2015). f(2012) = [Select] f(2015): =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…The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x)=64x-0.020x² 0≤x≤3200 (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. 23 (Round to one decimal place as needed.) (B) R'(x) =
- A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are related by s = 30.000 - 20.000 e -0.00025x. The current weekly advertising costs are $4,000, and these costs are increasing at a rate of $600 per week. Find the current rate of change of sales. The current rate of change of sales is $ per week. (Round to the nearest dollar as needed.)Can you help me find C(x) ?Cost of buying tomato plants are 20 cents each and a farmer sells them for 50 cents each. His fixed costs are euro 60 including the rate he pays to the local council. How many tomato plants must he sell to break even? What kind of profit will he realize from selling 180 plants? Formulate P(x) function clearly and graph it. Values of its intersections with both axes must be clear.