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Introduction to Management Science 12th Edition by Bernard Taylor
Edition 12ISBN: 978-0133778847Introduction to Management Science 12th Edition by Bernard Taylor
Edition 12ISBN: 978-0133778847 Exercise 54
In Problem 37 in Chapter, when Tracy McCoy wakes up Saturday morning, she remembersthat she promised the PTA she would make some cakes and/or homemade bread for its bake salethat afternoon
In Problem in Chapter, when Tracy McCoy wakes up Saturday morning, she remembers that she promised the PTA she would make some cakes and/or homemade bread for its bake sale that afternoon. However, she does not have time to go to the store to get ingredients, and she has only a short time to bake things in her oven. Because cakes and breads require different baking temperatures, she cannot bake them simultaneously, and she has only 3 hours available to bake. A cake requires 3 cups of flour, and a loaf of bread requires 8 cups; Tracy has 20 cups of flour. A cake requires 45 minutes to bake, and a loaf of bread requires 30 minutes. The PTA will sell a cake for $10 and a loaf of bread for $6. Tracy wants to decide how many cakes and loaves of bread she should make.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.
Problem
Assume that the objective function in Problem has been changed from Z = 30 x 1 + 70 x 2 to Z = 90 x 1 + 70 x 2. Determine the slope of each objective function and discuss what effect these slopes have on the optimal solution.
Problem
A manufacturing firm produces two products. Each product must undergo an assembly process
and a finishing process. It is then transferred to the warehouse, which has space for only a limited number of items. The firm has 80 hours available for assembly and 112 hours for finishing, and it can store a maximum of 10 units in the warehouse. Each unit of product 1 has a profit of $30 and requires 4 hours to assemble and 14 hours to finish. Each unit of product 2 has a profit of $70 and requires 10 hours to assemble and 8 hours to finish. The firm wants to determine the quantity of each product to produce in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis
In Problem in Chapter, when Tracy McCoy wakes up Saturday morning, she remembers that she promised the PTA she would make some cakes and/or homemade bread for its bake sale that afternoon. However, she does not have time to go to the store to get ingredients, and she has only a short time to bake things in her oven. Because cakes and breads require different baking temperatures, she cannot bake them simultaneously, and she has only 3 hours available to bake. A cake requires 3 cups of flour, and a loaf of bread requires 8 cups; Tracy has 20 cups of flour. A cake requires 45 minutes to bake, and a loaf of bread requires 30 minutes. The PTA will sell a cake for $10 and a loaf of bread for $6. Tracy wants to decide how many cakes and loaves of bread she should make.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.
Problem
Assume that the objective function in Problem has been changed from Z = 30 x 1 + 70 x 2 to Z = 90 x 1 + 70 x 2. Determine the slope of each objective function and discuss what effect these slopes have on the optimal solution.
Problem
A manufacturing firm produces two products. Each product must undergo an assembly process
and a finishing process. It is then transferred to the warehouse, which has space for only a limited number of items. The firm has 80 hours available for assembly and 112 hours for finishing, and it can store a maximum of 10 units in the warehouse. Each unit of product 1 has a profit of $30 and requires 4 hours to assemble and 14 hours to finish. Each unit of product 2 has a profit of $70 and requires 10 hours to assemble and 8 hours to finish. The firm wants to determine the quantity of each product to produce in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis
Explanation
Verified
Verified
(a)
Formulate the linear programming equ...
Introduction to Management Science 12th Edition by Bernard Taylor
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