Explanation Given: (a) The dealer D 1 needs at least 32 computers. (b) The dealer D 2 needs at least 20 computers. (c) The two warehouses W 1 and W 2 have 25 and 30 computers in hand, respectively. (d) The shipment cost per computer is given by Dealers D 1 D 2 Warehouse W 1 $14 $12 W 2 $12 $10 Explanation: Let x 1 be the total number of computers supplied by W 1 to the distributor D 1 . Let x 2 be the total number of computers supplied by W 1 to the distributor D 2 . Let x 3 be the total number of computers supplied by W 2 to the distributor D 1 . Let x 4 be the total number of computers supplied by W 2 to the distributor D 2 . Use the given statements to form the following system of linear equalities: x 1 + x 3 ≥ 32 x 2 + x 4 ≥ 20 x 1 + x 2 ≤ 25 x 3 + x 4 ≤ 30 The objective function to be minimized is 14 x 1 + 12 x 2 + 12 x 3 + 10 x 4 = z . Assume an objective function w such that w = − z . Then the maximum value of w will be equal to the minimum value of z . Introduce slack variables c 1 and c 2 . Introduce surplus variables c 3 and c 4 . The system of linear inequalities becomes x 1 + x 3 − c 1 = 32 x 2 + x 4 − c 2 = 20 x 1 + x 2 + c 3 = 25 x 3 + x 4 + c 4 = 30 and w + 14 x 1 + 12 x 2 + 12 x 3 + 10 x 4 = 0 Also x 1 , x 2 , x 3 , x 4 ≥ 0 This produces a tableau given by [ x 1 x 2 x 3 x 4 c 1 c 2 c 3 c 4 z 1 0 1 0 − 1 0 0 0 0 32 0 1 0 1 0 − 1 0 0 0 20 1 1 0 0 0 0 1 0 0 25 0 0 1 1 0 0 0 1 0 30 14 12 12 10 0 0 0 0 1 0 ] _ In this case, the basic variable c 1 is negative; hence, choose an element farthest from the left to make it a pivot element. Use the ratio test to find the pivot: 30 1 = 30 , 25 1 = 25 Therefore, 1 is the pivot as the least positive ratio is obtained for this element. Use the first element in the third row as the pivot. Use row operations R 1 − R 3 → R 1 , R 5 − 14 R 3 → R 5 to change all the remaining elements in the pivot column to 0. [ x 1 x 2 x 3 x 4 c 1 c 2 c 3 c 4 z 0 − 1 1 0 − 1 0 − 1 0 0 7 0 1 0 1 0 − 1 0 0 0 20 1 1 0 0 0 0 1 0 0 25 0 0 1 1 0 0 0 1 0 30 0 − 2 12 10 0 0 − 14 0 1 − 350 ] _ The basic variable c 1 is negative; hence, choose the positive entry farthest on the left on the first row. Use ratio test to find the pivot: 7 − 1 = − 7 , 20 1 = 20 , 25 1 = 25 Therefore, 1 is the pivot as the least positive ratio is obtained for this element. Use the second element in the second row as the pivot. Use row operation R 1 + R 2 → R 1 , R 3 − R 2 → R 3 , R 5 + 2 R 2 → R 5 to change all the remaining elements in the pivot column to 0

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133886818

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

Publisher: PEARSON

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Chapter 4.4, Problem 25E

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The way order is placed so that the shipment cost is minimum.

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Chapter 4.4, Problem 24E

Chapter 4.4, Problem 26E

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Chapter 4 Solutions

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 2E Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 4E Ch. 4.1 - For Exercises 5-8. (a) determine the number of...Ch. 4.1 - Prob. 6E Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - Introduce slack variables as necessary, then...Ch. 4.1 - Introduce slack variables as necessary, then write...

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The way order is placed so that the shipment cost is minimum.

Solution Summary: The author explains how to determine the minimum shipment cost of two computers to a dealer. The two warehouses have 25 and 30 computers in hand.

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