A utility function is given as                         S (n) = - (n – 4)2 + 15             where S (n) = the utility level for a certain n amount of an item. Use calculus (not trial and error) to determine the n value which will maximize the S value, and the S value itself.

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

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Q: 10. Jingle Bells Inc. has received a rush order for as many of two types of Easter eggs as can be…

A: Step:-1 Given profit function is Px1, x2 = -x12 - x22 +12x1 +10x2 +61 Here,  x1= thousands of units…

Q: Consider the following. = -0.1s3 + 6s² + 400 Find the amount s of advertising (in thousands of…

A: The point of diminishing returns refers to the inflection point of a return function or the maximum…

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Q: n entrepreneur starts new companies and sells them when their growth is maximized. Suppose that the…

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Q: iv. Determine the level of output for which the firm's profit is maximized. v. What is the firms's…

A: d) Find the first and second derivative using the power rule

Q: The profit function for good x is given by P(q) = 200 + 1009 + 30q²-9² where q is the quantity of x…

A: It is provided that the profit function is P(q)=200+100q+30q2-13q3. We need to determine the maximum…

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A: Solution

Q: What is the maximum profit when the profit-versus-production function is as given below? P is profit…

A: topic - maximum value

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

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Q: The demand function for a monopolist's product is p= 500 If the monopolist wants to produce at least…

A: Given p=500-q

Q: uppose that an appliance maker determines that in order to sell q appliances, the price per appli-…

A: According to our guideline we can only answer first three subparts.

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Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) = – 0.03q² + 3q – 35, where q…

A: Given profit function-P(q)=-0.03q2+3q-35 (A) To find pair of sunglasses (in thousands ) should be…

Q: For a certain company, the cost function for producing x items is C(x)=50x+100 and the revenue…

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Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) = – 0.02g? + 3q – 22, where q…

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Q: Consider the following. P = -0.1s3 + 6s2 + 400 Find the amount s of advertising (in thousands of…

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Q: Wutz UpDogs,Inc., supplies hot dogs to sport stadiums. The total profit function per game is given…

A: The answer is found in step-2.

Q: Suppose a tour guide has a bus that holds a maximum of 100 people. Assume his profit (in dollars)…

A: P(n) = n(50 - 0.5n) - 100 P(n) = 50n - 0.5n2 - 100 Domain : [ 0,100 ] Now, P'(n) = 50 - n  To Find…

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Q: 6. The total profit P(x) in thousands of dollars from the sale of x units of a certain prescription…

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Q: Wutz UpDogs chose a particular football stadium to test market a new jumbo hot dog. It was found…

A: Given that x denotes the number of hot dogs sold during one game in thousands and p denotes the…

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: A fertilizer producer finds that it can sell its product at a price of p 300– 0.1r dollars per unit…

A: It is given that, total cost for x units, C(x)=15000-125x+0.025x2 price per unit is, p(x)=300-0.1x…

Q: For a particular financial methodology, the risk-reward function was defined as y=x(Inx-2), where y…

A: The risk-reward function,    y=xlnx-2y=units of reward, x=units of risk

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

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Q: Consider the following. P = -0.1s3 + 6s² + 400 Find the amount s of advertising (in thousands of…

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Q: The demand function for a product is modeled by - 13,00(1- p3D 6 + e-0.001x Find the pricep (in…

A: a) The demand function is given as p=130001-66+e-0.001x when x=1000 p=130001-66+e-0.001×1000…

Q: 1. Assuming that the company sells all that it produces, what is the profit function? P (x) = 因团,…

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

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Q: For a certain company, the cost function for producing x items is C(x)=40x+200 and the revenue…

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Q: A piece of cardboard measuring 9 inches by 12 inches is formed into an open-top box by cutting…

A: Given:- A piece of cardboard measuring 9 inches by 12 inches is formed into an open-top box by…

Q: The manufacturing laundry sinks has fixed costs if $100 per day but has total costs of $2,500 per…

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Q: Wutz UpDogs, Inc., supplies hot dogs to sport stadiums. The total profit function per game is given…

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Q: Find the number in the interval (-1, -0.25) so that the sum of that number and its square is…

A: Let the function be fx=x+x2 and interval −1,−0.25. In order to function have maximized,…

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

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Q: e monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt.…

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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:

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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: Let q = demand for seats on a 500-seat airplane and p = price charged per ticket. Suppose that q =…

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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: All units in a 100-unit apartment building are rented out when the monthly rent is set at r =…

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

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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 => x= 1600

Q: Analysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y…

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Q: A time study showed that, on average, the productivity of a worker after t hours on the job can be…

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Q: The profit in dollars from the sale of x expensive watches is P(x) = 0.02x - 4x + 4x.6 - 4900. Find…

A: We know that Marginal profit is the derivative of the profit function.

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Q: y fx) 4 3 21 -5-4-3-2-1 x- 1 2 3 4 5 -2 On what interval(s) is fincreasing? How about decreasing? 1.

A: Let's find.