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- Differentiate the following function: y = (10x – 3)? O Y'= 20( x - 3) O Y'= 20(10x+3) O Y'= 20(10x-3) O Y'= 2 (10x-3)Let Var(X) = 25 and Z= 2X + 5 Compute Var (Z)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) =
- It is known that a certain company sells each kg of the product it manufactures at $80, it is also known that the total manufacturing cost "CT" is given by the function CT=(1/1000)x2 +100 , where "x" are the kg of product produced. a) How many units of "x" must the company sell to break even? Value = 100 points.b) How many units of "x" is the optimal quantity that should be sold to optimize the producer's profit? Value = 100 points.c) How many monetary units does that optimal profit for producers amount to? (remember, you will have to prove it mathematically either by the method of the first or by the method of the second derivative). Value = 100 points.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? $A store owner specializes in connoisseur coffee blends and wants to make 1 kilogram bags that will sell for $ 120 using Colombian, Brazilian and Kenyan coffees. The cost per kilogram of these three types of coffee is $ 140, $ 70, $ 100, respectively. x=Colombian y=Brazilian z=Kenyan Find: The solution of the system of linear equations:
- Given the functional relationship: y = 14x5/x2 find the value of y when x = 1.5Qs = 89830 -40PS +20PX +15PY +2I +.001A +10W Are X’s sailboats a substitute for or complementary to Smooth Sailing sailboats? What feature of the function tells you? Are Y’s motorboats a substitute for or complementary to Smooth Sailing sailboats? What feature of the function tells you?Find the maximum of the function f defined as f(x) = 4x - 2x2 - 110 A
- 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.Could I have some help deriving the solutions? I’m confused given that it isn’t a standard cobb Douglas function(1) If you have been hired at an annual salary of $23,000 and expect to receive annual increases of 5%, what will your salary be when you begin your seventh year? 3x (2) Determine the inverse of the function f(x)= 2x–5 (3) Ladders used by fruit pickers are typically tapered with a wide bottom for stability and a narrow top for ease of picking. If the bottom rung of such a ladder is 49 inches wide and the top rung is 19 inches wide. Stating explicitly the formulae used, determine: (i) How many rungs does the ladder have if each rung is 2.5 inches shorter than the one below it? (ii) How much material would be needed to make the rungs for the ladder described?