Practice Math Optimization Problems Fully Solved And Graded A+ Guaranteed Success/2024.
Find two positive real numbers such that the sum of the first two number squared and the second number is 48 and their product is a maximum. - correct answer 1. x² + y = 48 y=48-x² 2. p(x) =xy p(x) = x(48-x²) 3. p'(x) = 48-3x² x²=16 x=+4,-4 x=4 4.y=32 Find two positive real numbers x and y such that their product is 800 and x +2y is as small as possible. - correct answer 1. xy = 800 2. s = x+2y s(x) =x + 2(800/x) s(x) = x + 1600/x 3. s'(x) = 1-1600/x² s'(x) 1=1600/x² x=40 y =20 Find dimensions x and y of the rectangle of maximum area that can be formed using 3 m of wire. - correct answer 1. 3m = 2x +2y 2. A = xy A(x) = x(3/2 - x) A(x) = 3/2x - x² 3. A'(x) = 3/2 -2x =0 3/4=x
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- Subido en
- 8 de mayo de 2024
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- 2
- Escrito en
- 2023/2024
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- Examen
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