Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Textbook Question

Chapter 4, Problem 19RE

For each problem, (a) add slack variables or subtract surplus variables, and (b) set up the initial simplex tableau.

19. Maximize z = 5 x 1 + 8 x 2 + 6 x 3 subject to: x 1 + x 2 + x 3 ≤ 90 2 x 1 + 5 x 2 + x 3 ≤ 120 x 1 + 3 x 2 ≥ 80 with x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0.

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Chapter 4, Problem 18RE

Chapter 4, Problem 20RE

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Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties to find lim→-4 1 [2h (x) — h(x) + 7 f(x)] : - h(x)+7f(x) 3 O DNE

17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t). (a) How much of the slope field can you sketch from this information? [Hint: Note that the differential equation depends only on t.] (b) What can you say about the solu- tion with y(0) = 2? (For example, can you sketch the graph of this so- lution?) y(0) = 1 y AN

(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Pro

Chapter 4 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 4.1 - Prob. 1YT Ch. 4.1 - Prob. 2YT Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - For Exercises 58, (a) determine the number of...Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E

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For each problem, (a) add slack variables or subtract surplus variables, and (b) set up the initial simplex tableau. 19. Maximize z = 5 x 1 + 8 x 2 + 6 x 3 subject to: x 1 + x 2 + x 3 ≤ 90 2 x 1 + 5 x 2 + x 3 ≤ 120 x 1 + 3 x 2 ≥ 80 with x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0.

Solution Summary: The author explains how to add the slack variable or subtract surplus variable in the linear programming problem.

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Chapter 4 Solutions