A company is increasing the production of a product at the rate of 20 units per week. The demand and cost functions for the product are given by  p = 60 − 0.03x  and  C = 4000 + 30x − 0.04x2,  where x is the number of units produced per week. Find the rate of change of the profit with respect to time (in dollars per week) when the weekly sales are  x = 800 units.

Q: A company has average monthly costs, in dollars, given by: C ̂ = 45000 / x + 100 + x Where x is the…

A:

Q: Suppose that a companys sales volume, y (in thousands of units) is related to its advertising…

A:

Q: At a manufacturing plant, the total cost to produce x items is given by the function c(x)=…

A: Marginal cost is the rate of change of total cost, i.e, c'(x).

Q: The cost of manufacturing snow blowers is given by C(x) = 350 + 6x - 0.4x². А. Find the marginal…

A: Solution B )average cost = ΔC / ΔX  = (350 + 6x - 0.4x2)/ x = 350/x + 6 - 0.4x at  x = 25 = 350/ 25…

Q: diau uonsann Suppose the average number of vehicles arriving at the main gate of an amusement park…

A: Answer: (a) The admittance is about 20 vehicles per minute. (nearest tenth value) (b) 3 attendants…

Q: Suppose that the profit (In dollars) from the sale of Kisses and Kreams is given by P(x, y) = 15x +…

A: Sale of Kisses Kreams is given by P(x, y)=15x+6.5y-0.004x2-0.015y2 where, x is the number of pounds…

Q: A company has determined that its price-demand function for its sale of its product is given by…

A:

Q: The demand function for a tablet is given by the model p = 200 - 16x2 where p is measured in dollars…

A: Formula for revenue =(price per unit)×(number of units) Profit=revenue-total cost. To solve the…

Q: The management of Ditton Industries has determined that the daily marginal revenue function…

A:

Q: Suppose that a companys sales volume, y (in thousands of units) is related to its auvertising…

A:

Q: A company has started selling a new type of smartphone at the price of $110 - 0.1 x where x is the…

A:

Q: The marginal cost (in dollars per box) of producing the xth box of HDMI cables is C'(x)=-…

A: To find the function of C(x) we integrate C'(x) c=integrating constant

Q: Given the revenue and cost functions R=32x−0.5x ^2and C=8x+14​, where x is the daily​ production,…

A: I am going to solve the given problem by using the given data and get the required result.

Q: The weekly demand for DVDS manufactured by Herald media Corporation is given by p =-.0005x +60,…

A: To find the revenue function, calculate Rx=x·p, where p=-0.0005x2+60.…

Q: Suppose that the demand x (in units) for a product is x = 5,000 – 50p, where p dollars is the market…

A: Given expenditure is: E=5000p-50p2

Q: Given a total-revenue function R(x) = 800/x - 0.2x and a total-cost function C(x) = 1600 (x +5)+…

A: Total-revenue function R(x)= 800x2-0.2x Total-cost function C(x)= 1600(x2+5)13+500 Profit function…

Q: The marginal revenue function of a good is given by MR = 275 – x – 0.3x². Find the percent of…

A: Given: The marginal revenue function MR=275-x-0.3x2. The production is increased from 10 units to 20…

Q: f the total revenue function for a blender is R(x) = 76x – 0.01x² where x is the number of units…

A: Given that

Q: The quantity of the demand per month of a certain accessory is related to the price (in pesos) per…

A: Introduction: Differentiation has a wide range of applications in many fields of mathematics. One…

Q: A company finds that the total cost of manufacturing a units of a certain product is given by C(x)…

A: We will find the required information as shown below

Q: The rate at which a ceratin disease spreads is proportional to the product of the percentage of the…

A: We have to find the rate R(t) at which disease spreads Constant of  Proportionality = 0.03 Percent…

Q: of change of profit with respect to time when 10 units are produced and

A: Given that : Revenue function ( R) = 5x - 0.1x2  Cost function( C)  = 2x + 2 Where x is the daily…

Q: The cost (in pesos) of producing x corkboards is given by x? + 20x + 500, while the price (in pesos)…

A:

Q: When no more than 110 units are produced, the cost (in dollars) of producing x units is given by…

A: Given: C(x)=0.2x3-25x2+1531x+25000

Q: The marginal cost of producing the  xthxth  PC is  C′(x)=10+(x^2/60000)  and the fixed cost is…

A: We know the derivative of total cost gives us the marginal cost. The total cost is the sum of fixed…

Q: The rate of change of the variable y with respect to x is equal to the expression 5x*-3e***. What is…

A: rate of change of variable y with respect to x is =dydx

Q: The quantity of the demand per month of a certain accessory is related to the price (in 500 pesos)…

A: Given that: The quantity of the demand per month of a certain accessory is related to the price per…

Q: The demand and supply functions for a certain brand of breath mints are demand =−20x + 150 and…

A:

Q: Suppose that the demand x (in units) for a product is x = 16,500 – 150p, where p dollars is the…

A: It will be max where dE/dp will be 0.

Q: The marginal cost of producing x tablet computer is c'(x)=140-0.04x+0.00002x^2. What is the cost of…

A: We have given The marginal cost: c'(x) = 140-0.04x+0.00002x^2.

Q: The cost of producing x boards is given by x2 + 20x + 500, while the price of each board if there is…

A:

Q: For the fast- food restaurant, the revenue function R(x)=60000x-x^2/20000 and cost function…

A: Given that

Q: Suppose the percent of males who enrolled in college within 12 months of high school graduation is…

A: Given:         Percent of males enrolled in college is    y= -0.126x + 55.72         Percent of…

Q: Suppose that the demand x (in units) for a product is x = 7,500 − 150p, where p dollars is the…

A: Given demand function x (in units) for a product  x=7500-150p where p dollars is the market price…

Q: currently 49 workers, find the instantaneous rate of change of monthly output with respect to the…

A: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units,    (40 ≤ x ≤ 60)  , where x…

Q: An accessories company finds that the cost and revenue, in dollars, of producing x belts is given by…

A:

Q: The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by x = (107 -…

A:

Q: Suppose we have a revenue function given by R(x)=3x^3−αx, where α is a constant. What would the…

A: Formula used:

Q: In times of crisis like the Covid-19 pandemic, the basic needs of humans become in demand. The…

A:

Q: Suppose that the monthly cost in dollars of mining a certain ore is related to the number of pieces…

A: Given, the cost equation is Where x is the number of the piece of equipment used. We have to the…

Q: The monthly total revenue from a certain product sales of x unit is given as: R(x) =12x – 0.01x²…

A:

Q: The cost (in rupees) of producing x pillows is given by x² + 20x + 500, while the price (in rupees)…

A:

Q: The supply function for a product is given by p=20+100√2x+4, where x is the number of units supplied…

A: The supply function for a product is given by p=20+1002x+4, where x is the number of units supplied…

Q: The demand function for a tablet is given by the model P= 200-16x2 where p is measured in dollars…

A:

Q: The cost (in dollars) of producing x corkboards is given by x2+20x+500, while the price (in dollars)…

A: According to question,Given Cost function,Let Cx = x2 + 20x + 500,andDemand Function,px = 100 - x

Q: The yield in bushels from a grove of orange trees is given by Y = x(1000 − x), where x is the…

A: Rewrite the given function as Y=1000x-x2. Compare the above function with the quadratic function…

Q: A firm has monthly average costs, in dollars, given by 41,000 + 300 + x where x is the number of…

A:

Q: Over the next 20 years, a company projects its continuous flow of revenue to be R(x) = 100e01z…

A: Consider the provided question,

Q: A manufacturer has determined that the cost in pesos of producing shirts is given by C(x) = 0.5x² –…

A: Given Cost Function C(x)=0.5x2-x+6200Where x represents the number of shirts produced daily.

Q: A firm has monthly average costs, in dollars, given by C = 40,000/x + 300 + x where x is the number…

A: Profit, P = (Sale price per unit - average cost per unit) x Number of units = [2,000 - (40,000/x +…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.