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Determine the maximum value for the objective function, Z = 5x +2y, subject to the following constraints, 2r+ys 50 x+2y2 40 5x-ys0 y>0

Determine the maximum value for the objective function, Z = 5x +2y, subject to the following constraints, 2r+ys 50 x+2y2 40 5x-ys0 y>0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine the maximum value for the objective function, Z = 5x+2y, subject to the following constraints, 1. 2x+ys 50 x+2y2 40 5x - ys0 y>0 2. Each month a store owner can spend at most RMI00,000 on PC's and laptops. A PC costs the store owner RM1000 and a laptop costs him RMI500. Each PC and laptop is sold for a profit of RM400 and RM700 respectively. The store owner estimates that at least 20 PC's but no more than 80 are sold each month. He also estimates that the number of laptops sold is at most double the PC's. Duc to market research, the sum of twice the laptops and PC's cannot be less than 80. (a) Determine the objective function and formulate the given information in the form of linear programming model. (b) Płot the graph and shade the feasible region satisfying the system of linear inequalities in part (a) on the graph paper. (c) How many PC's and laptops should be sold in order to maximize the profit?
Transcribed Image Text:Determine the maximum value for the objective function, Z = 5x+2y, subject to the following constraints, 1. 2x+ys 50 x+2y2 40 5x - ys0 y>0 2. Each month a store owner can spend at most RMI00,000 on PC's and laptops. A PC costs the store owner RM1000 and a laptop costs him RMI500. Each PC and laptop is sold for a profit of RM400 and RM700 respectively. The store owner estimates that at least 20 PC's but no more than 80 are sold each month. He also estimates that the number of laptops sold is at most double the PC's. Duc to market research, the sum of twice the laptops and PC's cannot be less than 80. (a) Determine the objective function and formulate the given information in the form of linear programming model. (b) Płot the graph and shade the feasible region satisfying the system of linear inequalities in part (a) on the graph paper. (c) How many PC's and laptops should be sold in order to maximize the profit?
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