The marketing department of a company has determined that if it spends a thousands of dollars onbillboard advertisements and y thousand dollars on magazine advertisements, the company's revenue (inthousands of dollars) will beR(x, y) = -0.05x² - 50y² + 3x + 3y + 3xyHow much money should this company spend on billboard advertisements and magazine advertisements tomaximize its revenue?Billboard: $Magazine: $The maximum revenue the company will attain is $

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Answered: The marketing department of a company…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q4. Find the domain of the equation x + 5 y Vx2 – 16
Tailgate Essentials sells two types of tailgate tents, one plain tent and one with a team logo. The profit from the sale of these tents is given by P(x,y) = 83x + 167y -0.16xy -0.21x2 -0.32y2 - 11800 dollars when $x is the price of the plain tent and $y is the price of a tent with the team logo. Check: P(40,60) = -332 (a) Write out the system of equations that can be used to find the critical point of P(x,y). Enter your answers as a comma-separated list. For example: 3x + 4y =7, 2x - y =5 (b) Find the critical point of P(x,y) . Round all values to the nearest cent (2 decimal places). The critical point occurs when plain tents are sold for $ Tents with the team logo are sold for $ The profit at this point is $ (c) Find the second partial derivatives matrix and the value of the determinant at the critical point of P(x,y). Do NOT round. Determinant:
The unit cost, in dollars, to produce each box of cat food is $3 and the fixed monthly costs are $22244. The price-demand function, in dollars per box, is p(x)= -2x +469 Where x is the number of boxes of cat food.
A triathlete on the swimming leg of a triathlon is 130.0 m from the shore (a). The triathlete's bike is 90.0 m from the shore on the land (b). The component of her distance from the bicycle along the shore line, (x + y in the diagram), is 174.1 m. Triathlete a X Water shoreline y b Land If the triathlete's running speed is 9.40 m/s and swimming speed is 1.504 m/s, calculate the value of x so that the triathlete reaches her bike in the least amount of time. Submit Answer Tries 0/12 Calculate the minimum time required to reach the bicycle. Submit Answer Tries 0/12
A marketing firm has calculated that the total profits P of a product with x-dollars invested in marketing can be modeled as P(x)=-8x2 +56x+17, where P(x) and x are both measured in hundreds of dollars. How much money should be invested in marketing to maximize profits?

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