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Follow the steps below to find the nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of the Indicated express Complete parts (a) through (f) below. x+y=250 and the product P = xy as large as possible. (a) Solve x+y=D250 for y. Type an equation.) (b) Substitute the result from part (a) into P=xy, the equation for the variable that is to be maximized. (Type an equation.) (c) Find the domain of P found in part (b). Type your answer in interval notation.) dP dP (d) Find Solve the equation dx = 0. dx dP dP and when =0, x= dx (Use a comma to separate answers as needed.) dx (e) Evaluate P at any solutions found in part (d), as well as at the endpoints of the domain found in part (c). To answer the first part, select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. There was one solution in part (d). For that solution, P = O B. There were two solutions in part (d). For the lesser value of x, P= For the greater value of x, P = Evaluate P at the endpoints of the domain. At the lower endpoint, P= At the upper endpoint, P=. (f) Give the maximum value of P, as well as the two numbers, x and y, whose product is that value. P = when x= and y =

Follow the steps below to find the nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of the Indicated express Complete parts (a) through (f) below. x+y=250 and the product P = xy as large as possible. (a) Solve x+y=D250 for y. Type an equation.) (b) Substitute the result from part (a) into P=xy, the equation for the variable that is to be maximized. (Type an equation.) (c) Find the domain of P found in part (b). Type your answer in interval notation.) dP dP (d) Find Solve the equation dx = 0. dx dP dP and when =0, x= dx (Use a comma to separate answers as needed.) dx (e) Evaluate P at any solutions found in part (d), as well as at the endpoints of the domain found in part (c). To answer the first part, select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. There was one solution in part (d). For that solution, P = O B. There were two solutions in part (d). For the lesser value of x, P= For the greater value of x, P = Evaluate P at the endpoints of the domain. At the lower endpoint, P= At the upper endpoint, P=. (f) Give the maximum value of P, as well as the two numbers, x and y, whose product is that value. P = when x= and y =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 82E
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Follow the steps below to find the nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of the indicated expression. Complete parts (a) through (f) below. x+y= 250 and the product P = xy as large as possible. (a) Solve x+y= 250 for y. (Type an equation.) (b) Substitute the result from part (a) into P =xy, the equation for the variable that is to be maximized. (Type an equation.) (c) Find the domain of P found in part (b). (Type your answer in interval notation.) dP (d) Find- Solve the equation dx dP = 0 dx dP dP =D0. x = dx and when (Use a comma to separate answers as needed.) dx (e) Evaluate P at any solutions found in part (d), as well as at the endpoints of the domain found in part (c). To answer the first part, select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. There was one solution in part (d). For that solution, P = O B. There were two solutions in part (d). For the lesser value of x, P = For the greater value of x, P= Evaluate P at the endpoints of the domain. At the lower endpoint, P= At the upper endpoint, P= (f) Give the maximum value of P, as well as the two numbers, x and y, whose product is that value. P = when x= and y =
Transcribed Image Text:Follow the steps below to find the nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of the indicated expression. Complete parts (a) through (f) below. x+y= 250 and the product P = xy as large as possible. (a) Solve x+y= 250 for y. (Type an equation.) (b) Substitute the result from part (a) into P =xy, the equation for the variable that is to be maximized. (Type an equation.) (c) Find the domain of P found in part (b). (Type your answer in interval notation.) dP (d) Find- Solve the equation dx dP = 0 dx dP dP =D0. x = dx and when (Use a comma to separate answers as needed.) dx (e) Evaluate P at any solutions found in part (d), as well as at the endpoints of the domain found in part (c). To answer the first part, select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. There was one solution in part (d). For that solution, P = O B. There were two solutions in part (d). For the lesser value of x, P = For the greater value of x, P= Evaluate P at the endpoints of the domain. At the lower endpoint, P= At the upper endpoint, P= (f) Give the maximum value of P, as well as the two numbers, x and y, whose product is that value. P = when x= and y =
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