A time study showed that, on average, the productivity of a worker after t hours on the job can be modeled by P ( t ) = 27 t + 6 t 2 − t 3 , 0 ≤ t ≤ 8 where P is the number of units produced per hour. After how many hours will productivity be maximized? What is the maximum productivity?

Q: Consider the following total revenue function for a hammer. R- 48x – 0.01x2 (a) The sale of how many…

A:

Q: A coffee shop finds that at the price of $3.00, demand for their popular cappuccino drink is 3000…

A: Given that: At price of $3.00, demand = 3000 cups a year.For every $0.25 decrease in price, demand…

Q: Suppose the amount of a certain drug in the bloodstream is modeled by C(t)=8te-0.2t ,then the…

A:

Q: Find the consumer's surplus if the demand for an item is given by D(x) = 72- x, assuming supply and…

A: solve the following

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A:

Q: True or False: The linear function y = mx + b, where m # 0 has no maximum value on any open…

A: The answer is True.

Q: Assume that the number of bacteria R(t) (in millions) present in a certain culture at time t (in…

A: Given:         R(t)=t2(t−18)+96t+1000

Q: 2. Of all numbers whose sum is 30, find the two that have the maximum product. That is, maximize Q =…

A: To Determine: of all numbers whose sum is 50 ,find the two that have the maximum product .That is…

Q: At a certain vineyard it is found that each grape vine produces about 10 lbs of grapes in a season…

A: To find the number of vines that should be planted to maximize grape production.

Q: Find positive numbers x and y, whose sum is 75, such that xy2 is maximized.

A: Positive numbers x and y,x+y=75xy2 is maximized

Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) = – 0.01q“ + 5q – 46, where q…

A: Make the derivative of profit function equal to zero for maximum profit.

Q: The Cobb-Douglas production function for a particular product is N(x,y) = 40xy2, where x is the…

A:

Q: The profit from producing n quilts per year is given by the function P(n)=−15n^2+270n−840, where P…

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Q: Given: g (x) 2x³ 3x² 12x + 13 At what value of a does g have a relative maximum value? 0 6 00 0-1 O…

A:

Q: Suppose the amount of a certain drug in the bloodstream is modeled by C(t)=8te-0.2t ,then the…

A:

Q: Suppose that the selling price p of an item for the quantity x sold is given by the function 1 -x +…

A: Topic:- algebra

Q: A company with a monopoly is able to control the price of its product by limiting supply. If the…

A:

Q: Find the 4th iteration value of an extremum (maximum/minimum value) of f(x) = 0.25sinh(2x) - bx² -…

A: The function given is as follows: fx=0.25sinh2x-bx2-cx+d Where, b=3, c=5, and d=6. Hence the…

Q: The total daily profit (in thousands of pesos)of a certain food company for the sale of ... x boxes…

A:

Q: Consider the production function:           Y = 0.75X + 0.0042X2 – 0.000023X3 (a) At what level of…

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Q: 7. Given the profit function P(x) = 500x –- where 100 x is number of units sold. Find x to get…

A:

Q: 1. Of all numbers whose sum is 70, find the two that have the maximum product. That is, maximize Q =…

A: Let such two numbers whose sum is 70 and have the maximum product are x and y. So, we have x+y=70…

Q: Consider the following total revenue function for a hammer. R = 20x – 0.01x2 (a) The sale of how…

A: We have given  Total revenue function of hammer  R = 20x - 0.01x2  a)  As, R = 20x - 0.01x2  Implies…

Q: Consider the following total revenue function for a hammer. R = 20x – 0.01x² (a) The sale of how…

A: The revenue function of the hammer is R = 20x-0.01x2.

Q: Consider the following total revenue function for a hammer. R = 24x – 0.01x2 (a) The sale of how…

A:

Q: Suppose that the selling price pp of an item for the quantity xx sold is given by the function…

A:

Q: If a resistor of R ohms is connected across a battery of E volts with internal resistance r ohms,…

A:

Q: Suppose that the selling price p of an item for the quantity x sold is given by the function 1 x +…

A: Given,  p=-16x+26

Q: of all real numbers x such that -3 < x < 5. (a) For what values of x does f have a relative maximum?…

A: at x=-3 and x=5 f is relative maximum

Q: The function f(x) = 4 – 7x* has an absolute maximum value of and this occurs at x equals

A:

Q: The graph of f(x) = mx - 3x - nx +5 has a relative maximum at (-1,12) and a point of (1 3) 2' 2…

A:

Q: | (1 – a*)dæ (1 — а?) а

A:

Q: Consider the following total revenue function for a hammer. R = 36x – 0.01x² (a) The sale of how…

A:

Q: A fast food restaurant hos a cost Production C(x) = ||x+120 and arevenue function R (x) = 5x,When…

A: Consider the profit function is P(x)=R(x)-C(x) when this function is more than 0 then company makes…

Q: 2. After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: Given query is to find the time at which concentration will be maximum.

Q: The number of oil changes per hour at Quick Lube is described by the following short-term production…

A: answer is in next step .

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A:

Q: Let p=(12-2x)^2 for 0≤x≤3 be the price at which x hundred units of a certain commodity will be sold,…

A: Given: P=(12-2x)2         for 0≤x≤3            Revenue   R(x)=xP(x) then    R(x)=x12-2x2…

Q: A company that produces cellular phones analyzes its production and finds that the profit P (in…

A: Given:Profit Function:

Q: Consider the following total revenue function for a hammer. R = 48x – 0.01lx² (a) The sale of how…

A:

Q: The number of people P(t) (in thousands) infected t months after an epidemic begins 5 - where…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly aks…

Q: Consider the following total revenue function for a hammer. R = 60x − 0.01x2 (a) The sale of how…

A: a) Consider the given revenue function:

Q: A camera company estimates that the demand function for its new consumer digital camera is p=312e^…

A:

Q: In an economic enterprise, the total amount T that is produced is a function of the amount n of a…

A: (a) The graph of the function is as follows: (b) Here, T(1.02)=-2(1.02)3+3(1.02)2+1.02…

Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: Given that, The price demand function is px=70-0.25x and the cost function is Cx=0.5x2+10x+800. We…

Q: A manufacturer determines that the profit P (in dollars) obtained by producing and selling x units…

A: Given:            Profit model:                              P(x,…

Q: Consider the following total revenue function for a hammer. R = 28x − 0.01x2 (a) The sale of how…

A: The given revenue function is Rx=28x-0.01x2. (a) It is known that the maximum value occurs at the…

Q: Consider the following total revenue function for a hammer. R = 44x – 0.01x²2 (a) The sale of how…

A: We have given the total revenue function for a hammer.              R = 44x - 0.01x2  We have to…

Q: Consider the following total revenue function for a hammer. R = 32x – 0.01x² (a) The sale of how…

A: a) R= 32x-0.01x^2 Differentiate with respect to x dR/dx = 32 -0.02x dR/dx=0 =&gt; x= 1600

Q: Consider the function f(x) = 4 – 6x?, – 3 < x < 2. - The absolute maximum value is and this occurs…

A: To find The absolute maximum and absolute minimum values of f(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.