We know that f(x) = 48x° +42.x° + 3.5x – 16x°. 61г — 16.52? | We have also been given the initial bounds of -1 and 4 with an error tolerance of 0.08 so we start with checking the values of f(x) at x = -1 and 4 as the lower bound and the upper bound respectively. To carry out the bisection method we form the following table where the iterations are repeated until Ɛ or the error tolerance is less than or equal to a value of 0.08. b f(a) f(b) c=(a+b)/2 f(c) Ɛ = b-a a -1 4 -187 -29562 1.5 -16.6875 -1 1.5 -187 -16.6875 0.25 0.3046875 2.5 0.304688 -16.6875 0.304688 0.24823 0.25 1.5 0.875 0.24822998 1.25 0.25 0.875 0.5625 0.312483788 0.625 0.304688 0.312484 0.40625 0.312412 0.312484 0.484375 0.25 0.5625 0.312411889 0.3125 0.40625 0.5625 0.31249994 0.15625 0.484375 0.5625 0.3125 0.312484 0.523438 0.312499696 0.078125 From these calculations at the error tolerance of .078 < 0.08 we get to know that the maximization of the above function will happen approximately between 0.48 and 0.56 with the approximate value of 0.3125.

We know that f(x) = 48x° +42.x° + 3.5x – 16x°. 61г — 16.52? | We have also been given the initial bounds of -1 and 4 with an error tolerance of 0.08 so we start with checking the values of f(x) at x = -1 and 4 as the lower bound and the upper bound respectively. To carry out the bisection method we form the following table where the iterations are repeated until Ɛ or the error tolerance is less than or equal to a value of 0.08. b f(a) f(b) c=(a+b)/2 f(c) Ɛ = b-a a -1 4 -187 -29562 1.5 -16.6875 -1 1.5 -187 -16.6875 0.25 0.3046875 2.5 0.304688 -16.6875 0.304688 0.24823 0.25 1.5 0.875 0.24822998 1.25 0.25 0.875 0.5625 0.312483788 0.625 0.304688 0.312484 0.40625 0.312412 0.312484 0.484375 0.25 0.5625 0.312411889 0.3125 0.40625 0.5625 0.31249994 0.15625 0.484375 0.5625 0.3125 0.312484 0.523438 0.312499696 0.078125 From these calculations at the error tolerance of .078 < 0.08 we get to know that the maximization of the above function will happen approximately between 0.48 and 0.56 with the approximate value of 0.3125.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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