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Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized a. Solve x + y = 75 for y. y= b. Substitute the result from part a into the equation P = x²y for the variable that is to be maximized. c. Find the domain of the function P found in part b. (Simplify your answer. Type your answer in interval notation.) d. Find Solve the equation dP dx dP X dx Solve the equation. =(Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). dP dx P(0) = (Simplify your answer.) Determine P(50) 66°F Mostly cloudy = 0. C...

Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized a. Solve x + y = 75 for y. y= b. Substitute the result from part a into the equation P = x²y for the variable that is to be maximized. c. Find the domain of the function P found in part b. (Simplify your answer. Type your answer in interval notation.) d. Find Solve the equation dP dx dP X dx Solve the equation. =(Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). dP dx P(0) = (Simplify your answer.) Determine P(50) 66°F Mostly cloudy = 0. C...

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
Problem 6SC: A company that makes and sells baseball caps has found that the total monthly cost C in dollars of...
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Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized a. Solve x + y = 75 for y. y= b. Substitute the result from part a into the equation P = x²y for the variable that is to be maximized. c. Find the domain of the function P found in part b. (Simplify your answer. Type your answer in interval notation.) dP d. Find Solve the equation X dx dP dx Solve the equation. =(Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). dP dx P(0) = (Simplify your answer.) Determine P(50) 66°F Mostly cloudy = 0.
Transcribed Image Text:Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized a. Solve x + y = 75 for y. y= b. Substitute the result from part a into the equation P = x²y for the variable that is to be maximized. c. Find the domain of the function P found in part b. (Simplify your answer. Type your answer in interval notation.) dP d. Find Solve the equation X dx dP dx Solve the equation. =(Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). dP dx P(0) = (Simplify your answer.) Determine P(50) 66°F Mostly cloudy = 0.
Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized UA dP dx Solve the equation. X= (Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). UA P(0) = (Simplify your answer.) Determine P(50). P(50) = (Simplify your answer.) Find P(75). P(75)= (Simplify your answer.) f. Give the maximum value of P, as well as the two numbers x and y for which x2y is that value. The maximum value of P is The values of x and y are x = 66°F Mostly cloudy =and y = Q C...
Transcribed Image Text:Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized UA dP dx Solve the equation. X= (Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). UA P(0) = (Simplify your answer.) Determine P(50). P(50) = (Simplify your answer.) Find P(75). P(75)= (Simplify your answer.) f. Give the maximum value of P, as well as the two numbers x and y for which x2y is that value. The maximum value of P is The values of x and y are x = 66°F Mostly cloudy =and y = Q C...
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