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Algebra: Structure And Method, Book 1

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter8: Introduction To Functions

Section8.8: Linear And Quadratic Functions

Problem 16OE

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In Problem a function and the graph of a feasible region are given. In each case, find both the maximum and minimum values of the function, if they exist, and the point at which each occurs.

Expert Solution

Given,

The corner points of the feasible region are $(4, 8), (20, 0) & (20, 32)$ .

Now at $(4, 8)$ ,

$\begin{array}{rcl} f & = & 7 (4) - 6 (8) \\ = & 28 - 48 \\ = & - 20 \end{array}$

At $(20, 0)$ ,

$\begin{array}{rcl} f & = & 7 (20) - 6 (0) \\ = & 140 - 0 \\ = & 140 \end{array}$

At $(20, 32)$ ,

$\begin{array}{rcl} f & = & 7 (20) - 6 (32) \\ = & 140 - 192 \\ = & - 52 \end{array}$

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