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Problem 3 The Lock and Co Hatters produces two types of hats, the panama hat and baseball cap. Each first type of hat which is the panama hat requires twice as much as labor time as the baseball cap. If all hats are baseball only, the company can produce a total of 500 hats a day. The market limits daily sales of the panama hat and baseball cap to 150 and 350 hats respectively. Assuming that the profits per hat are Rs. 8 for panama hat and Rs. 5 for baseball cap. Formulate the problem as a linear programming model in order to determine the number of hats to be produced of each type so as to maximize the profit. Solution: Data Summary Chart Market Demand Variable Labor Profit per Hat Resource Unit Time Hats (Rs.) Limit 150 (max) 250 (max) Panama Hat 150 8 Baseball Cap 1 250 Decision Variables: x, = Panama Hat x, = Baseball Cap Objective Functions: Maximize (z) = 8x, + 5x, Constraints: Market Constraints: 2x, + x, s 500 Panama Hat Sales Constraints: X, s 150 Baseball Cap Sales Constraints: X, s 250 Non- Negativity: where: x,, X, 2 0

Problem 3 The Lock and Co Hatters produces two types of hats, the panama hat and baseball cap. Each first type of hat which is the panama hat requires twice as much as labor time as the baseball cap. If all hats are baseball only, the company can produce a total of 500 hats a day. The market limits daily sales of the panama hat and baseball cap to 150 and 350 hats respectively. Assuming that the profits per hat are Rs. 8 for panama hat and Rs. 5 for baseball cap. Formulate the problem as a linear programming model in order to determine the number of hats to be produced of each type so as to maximize the profit. Solution: Data Summary Chart Market Demand Variable Labor Profit per Hat Resource Unit Time Hats (Rs.) Limit 150 (max) 250 (max) Panama Hat 150 8 Baseball Cap 1 250 Decision Variables: x, = Panama Hat x, = Baseball Cap Objective Functions: Maximize (z) = 8x, + 5x, Constraints: Market Constraints: 2x, + x, s 500 Panama Hat Sales Constraints: X, s 150 Baseball Cap Sales Constraints: X, s 250 Non- Negativity: where: x,, X, 2 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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Solve the optimization problem using linear programming. Find the optimal solution with graph.

Problem 3 The Lock and Co Hatters produces two types of hats, the panama hat and baseball cap. Each first type of hat which is the panama hat requires twice as much as labor time as the baseball cap. If all hats are baseball only, the company can produce a total of 500 hats a day. The market limits daily sales of the panama hat and baseball cap to 150 and 350 hats respectively. Assuming that the profits per hat are Rs. 8 for panama hat and Rs. 5 for baseball cap. Formulate the problem as a linear programming model in order to determine the number of hats to be produced of each type so as to maximize the profit. Solution: Data Summary Chart Market Demand Variable Labor Profit per Hat Resource Unit Time Hats (Rs.) Limit 150 (max) 250 (max) Panama Hat 150 8 Baseball Cap 1 250 Decision Variables: x, = Panama Hat x, = Baseball Cap Objective Functions: Maximize (z) = 8x, + 5x, Constraints: Market Constraints: 2x, + x, s 500 Panama Hat Sales Constraints: X, s 150 Baseball Cap Sales Constraints: X, s 250 Non- Negativity: where: x,, X, 2 0
Transcribed Image Text:Problem 3 The Lock and Co Hatters produces two types of hats, the panama hat and baseball cap. Each first type of hat which is the panama hat requires twice as much as labor time as the baseball cap. If all hats are baseball only, the company can produce a total of 500 hats a day. The market limits daily sales of the panama hat and baseball cap to 150 and 350 hats respectively. Assuming that the profits per hat are Rs. 8 for panama hat and Rs. 5 for baseball cap. Formulate the problem as a linear programming model in order to determine the number of hats to be produced of each type so as to maximize the profit. Solution: Data Summary Chart Market Demand Variable Labor Profit per Hat Resource Unit Time Hats (Rs.) Limit 150 (max) 250 (max) Panama Hat 150 8 Baseball Cap 1 250 Decision Variables: x, = Panama Hat x, = Baseball Cap Objective Functions: Maximize (z) = 8x, + 5x, Constraints: Market Constraints: 2x, + x, s 500 Panama Hat Sales Constraints: X, s 150 Baseball Cap Sales Constraints: X, s 250 Non- Negativity: where: x,, X, 2 0
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