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Assume that the Natural Fertilizer Company produces 100 pound sacks of 20-15-20 fertilizer for lawns, 100 pound sacks of 11-12-8 fertilizer for gardens, and 100 pound sacks of 4-8-6 fertilizer for trees, where the numbers are the percentage by weight of nitrate, phosphate, and potash, respectively, in each sack. Assume also that the company has on hand 12 tons of nitrate, 9 tons of phosphate, and 8 tons of potash, Assume also that the profit on each sack of lawn fertilizer is $10.00, the profit on each sack of garden fertilizer is $6.00, and the profit on each sack of tree fertilizer is $5.00. Finally, assume the company has a contract to supply at least 2.5 tons of garden fertilizer. How many sacks of each type of fertilizer should the company make in order maximize its profit? When you formulate a linear programming problem to solve this problem, how many variables, how many constraints (both implicit and explicit), and how many objective functions should you have? Number of variables: 3 Number of constraints: 7 Number of objective functions: 1 • Part 2 - Part 3 Formulate the linear programming problem for this situation. (Enter either the word Maximize or the word Minimize in the first blank. Type the symbols <= wherever you want a "less than or equal" inequality, i.e., <, and type the symbols >= wherever you what a "greater than or equal" inequality, i.e., >.) x+ y+ z (in dollars) subject to the constraints nitrate used (in pounds): y+ pounds phosphate used (in pounds): yt pounds potash used (in pounds): x + y+ pounds supply contract (in pounds): x+ y+ pounds |曲

Assume that the Natural Fertilizer Company produces 100 pound sacks of 20-15-20 fertilizer for lawns, 100 pound sacks of 11-12-8 fertilizer for gardens, and 100 pound sacks of 4-8-6 fertilizer for trees, where the numbers are the percentage by weight of nitrate, phosphate, and potash, respectively, in each sack. Assume also that the company has on hand 12 tons of nitrate, 9 tons of phosphate, and 8 tons of potash, Assume also that the profit on each sack of lawn fertilizer is $10.00, the profit on each sack of garden fertilizer is $6.00, and the profit on each sack of tree fertilizer is $5.00. Finally, assume the company has a contract to supply at least 2.5 tons of garden fertilizer. How many sacks of each type of fertilizer should the company make in order maximize its profit? When you formulate a linear programming problem to solve this problem, how many variables, how many constraints (both implicit and explicit), and how many objective functions should you have? Number of variables: 3 Number of constraints: 7 Number of objective functions: 1 • Part 2 - Part 3 Formulate the linear programming problem for this situation. (Enter either the word Maximize or the word Minimize in the first blank. Type the symbols <= wherever you want a "less than or equal" inequality, i.e., <, and type the symbols >= wherever you what a "greater than or equal" inequality, i.e., >.) x+ y+ z (in dollars) subject to the constraints nitrate used (in pounds): y+ pounds phosphate used (in pounds): yt pounds potash used (in pounds): x + y+ pounds supply contract (in pounds): x+ y+ pounds |曲

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 11P
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• Part 1 Assume that the Natural Fertilizer Company produces 100 pound sacks of 20-15-20 fertilizer for lawns, 100 pound sacks of 11-12-8 fertilizer for gardens, and 100 pound sacks of 4-8-6 fertilizer for trees, where the numbers are the percentage by weight of nitrate, phosphate, and potash, respectively, in each sack. Assume also that the company has on hand 12 tons of nitrate, 9 tons of phosphate, and 8 tons of potash, Assume also that the profit on each sack of lawn fertilizer is $10.00, the profit on each sack of garden fertilizer is $6.00, and the profit on each sack of tree fertilizer is $5.00. Finally, assume the company has a contract to supply at least 2.5 tons of garden fertilizer. How many sacks of each type of fertilizer should the company make in order maximize its profit? When you formulate a linear programming problem to solve this problem, how many variables, how many constraints (both implicit and explicit), and how many objective functions should you have? Number of variables: 3 Number of constraints: 7 Number of objective functions: 1 • Part 2 • Part 3 Formulate the linear programming problem for this situation. (Enter either the word Maximize or the word Minimize in the first blank. Type the symbols <= wherever you want a "less than or equal" inequality, i.e., <, and type the symbols >= wherever you what a "greater than or equal" inequality, i.e., >.) x+ y+ z (in dollars) subject to the constraints nitrate used (in pounds): x + y+ pounds phosphate used (in pounds): x + y+ pounds potash used (in pounds): x + yt pounds supply contract (in pounds): x + y+ pounds 曲 א וא א א
Transcribed Image Text:• Part 1 Assume that the Natural Fertilizer Company produces 100 pound sacks of 20-15-20 fertilizer for lawns, 100 pound sacks of 11-12-8 fertilizer for gardens, and 100 pound sacks of 4-8-6 fertilizer for trees, where the numbers are the percentage by weight of nitrate, phosphate, and potash, respectively, in each sack. Assume also that the company has on hand 12 tons of nitrate, 9 tons of phosphate, and 8 tons of potash, Assume also that the profit on each sack of lawn fertilizer is $10.00, the profit on each sack of garden fertilizer is $6.00, and the profit on each sack of tree fertilizer is $5.00. Finally, assume the company has a contract to supply at least 2.5 tons of garden fertilizer. How many sacks of each type of fertilizer should the company make in order maximize its profit? When you formulate a linear programming problem to solve this problem, how many variables, how many constraints (both implicit and explicit), and how many objective functions should you have? Number of variables: 3 Number of constraints: 7 Number of objective functions: 1 • Part 2 • Part 3 Formulate the linear programming problem for this situation. (Enter either the word Maximize or the word Minimize in the first blank. Type the symbols <= wherever you want a "less than or equal" inequality, i.e., <, and type the symbols >= wherever you what a "greater than or equal" inequality, i.e., >.) x+ y+ z (in dollars) subject to the constraints nitrate used (in pounds): x + y+ pounds phosphate used (in pounds): x + y+ pounds potash used (in pounds): x + yt pounds supply contract (in pounds): x + y+ pounds 曲 א וא א א
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