Explanation Given information: Customer A needs 50 sheets and customer B needs 70 sheets. The west side store has 45 sheets and the east side store has 80 sheets. The delivery cost per sheet for the east-side store to customer A is $ 0.50 and to the customer B is $ 0.60 and the delivery cost per sheet for the west-side store to customer A is $ 0.40 and to the customer B is $ 0.55 . Calculation: Consider the number of sheet to be shipped from east-side store to customer A be x and the number of sheets to be shipped from east-side store to customer B be y . The number of sheets the customer A needs is 50 and customer B needs 70 sheets. Therefore, the number of sheets to be shipped from west side store to customer A is 50 − x and the sheets to be shipped from west-side store to customer B is 70 − x . The delivery cost per sheet for the east-side store to customer A is $ 0.50 and to the customer B is $ 0.60 and the delivery cost per sheet for the west-side store to customer A is $ 0.40 and to the customer B is $ 0.55 . P = 0.5 x + 0.6 y + 0.4 ( 50 − x ) + 0.55 ( 70 − y ) = 0.5 x + 0.6 y + 20 − 0.4 x + 38.5 − 0.55 y Simplify the above equation as, P = 0.1 x + 0.05 y + 58.5 …… (1) The number of sheets to be shipped from east side store to customers cannot be negative. x ≥ 0 and y ≥ 0 The number of sheets to be shipped from west-side store to customers cannot be negative. 50 − x ≥ 0 and 70 − y ≥ 0 Simplify the inequality 50 − x ≥ 0 and 70 − y ≥ 0 as, x ≤ 50 and y ≤ 70 The inequality x ≥ 0 and the inequality x ≤ 50 can be combined as, 0 ≤ x ≤ 50 …… (2) The inequality y ≥ 0 and the inequality y ≤ 70 can be combined as, 0 ≤ y ≤ 70 …… (3) The east side store has 80 sheets. x + y ≤ 80 …… (4) The west-side store has 45 sheets. 50 − x + 70 − y ≤ 45 120 − x − y ≤ 45 − x − y ≤ 45 − 120 − x − y ≤ − 75 Simplify the above inequality as, x + y ≥ 75 …… (5) Therefore, x and y must satisfy the constraints as, { 0 ≤ x ≤ 50 0 ≤ y ≤ 70 x + y ≤ 80 x + y ≥ 75 From inequality x ≥ 0 and y ≥ 0 it is observed that the solution set lies in I quadrant. The graph of the inequalities 0 ≤ x ≤ 50 , 0 ≤ y ≤ 70 , x + y ≤ 80 and x + y ≥ 75 is shown in Figure 1. From Figure 1 it is observed that the solution set is represented by the darkest shade. The corresponding equation of inequality (2) can be expressed as, x = 50 …… (6) The corresponding equation of inequality (3) can be expressed as, y = 70 …… (7) The corresponding equation of inequality (4) can be expressed as, x + y = 80 …… (8) The corresponding equation of inequality (5) can be expressed as, x + y = 75 …… (9) Substitute 50 for x in equation (8) to obtain the value of y as, 50 + y = 80 y = 80 − 50 = 30 The intersection of the lines x = 50 and x + y = 80 is the point ( 50 , 30 ) . Substitute 70 for y in equation (8) to obtain the value of x as, x + 70 = 80 x = 80 − 70 = 10 The intersection of the lines y = 70 and x + y = 80 is the point ( 10 , 70 )

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 5, Problem 10P

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The number of sheets to be shipped from east side to customer A, east side to customer B, west side to customer A and west side to customer B to minimize the delivery cost.

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Chapter 5, Problem 9P

Chapter 5, Problem 11P

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Chapter 5 Solutions

College Algebra

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The number of sheets to be shipped from east side to customer A, east side to customer B, west side to customer A and west side to customer B to minimize the delivery cost.

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To calculate: The number of sheets to be shipped from east side to customer A, east side to customer B, west side to customer A and west side to customer B to minimize the delivery cost.

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Chapter 5 Solutions

To calculate:

The number of sheets to be shipped from east side to customer A, east side to customer B, west side to customer A and west side to customer B to minimize the delivery cost.