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

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...

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