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manufacturing-Production Planning A mining company owns 2 different mines that produce ore, which is crushed and graded into three classes: high, medium, and low grade. The company has a contract to provide a smelting plant with at least 13 tons of high-grade, 9 tons of medium-grade, and 24 tons of low-grade ore per week. The two mines have different operating characteristics, as outlined in the table below: Mine #Tons/Day Low 4 6 #Tons/Day High 3 2 #Tons/Day Medium 3 1 #1 #2 The operating costs for Mine #1 are $12,000 per day and the operating costs for Mine # 2 are $10,000 per day. Each mine operates at most 5 days per week. How many days per week should each mine operate to meet or exceed the smelting plant contract and minimize the total cost? Let x = the number of days per week that Mine 1 operates per week, and Lety - the number of days per week that Mine 2 operates per week Which option (a, b, c, or d) shows the correct objective function and constraints for this application? O Objective Function: Minimize Cost, C-12000x+10000y Constraints: 3x + 2y >= 9,3x+y>= 13, 4x+6y= 24, x <= 5, y <= 5, x>0, y = 0 O Objective Function: Minimize Cost, C-12000x+10000y Constraints: 3x + 2y >= 13, 3x+y>= 9, 4x+6y>= 24, x <= 5, y <= 5, x>= 0, y = 0 O Objective Function: Minimize Cost, C-12000x+10000 Constraints: 3x + 2y > 13, 3x + y 24, 4x+6y>-9, x <= 5, y < 5₁ x >= 0, y = 0 O Objective Function: Minimize Cost, C = 12000x+10000y Constraints: 3x + 2v>= 24 3x+v># 13, 4x+6y>=9₁ x <= 5.v<= 5.x >=0.v> 0

manufacturing-Production Planning A mining company owns 2 different mines that produce ore, which is crushed and graded into three classes: high, medium, and low grade. The company has a contract to provide a smelting plant with at least 13 tons of high-grade, 9 tons of medium-grade, and 24 tons of low-grade ore per week. The two mines have different operating characteristics, as outlined in the table below: Mine #Tons/Day Low 4 6 #Tons/Day High 3 2 #Tons/Day Medium 3 1 #1 #2 The operating costs for Mine #1 are $12,000 per day and the operating costs for Mine # 2 are $10,000 per day. Each mine operates at most 5 days per week. How many days per week should each mine operate to meet or exceed the smelting plant contract and minimize the total cost? Let x = the number of days per week that Mine 1 operates per week, and Lety - the number of days per week that Mine 2 operates per week Which option (a, b, c, or d) shows the correct objective function and constraints for this application? O Objective Function: Minimize Cost, C-12000x+10000y Constraints: 3x + 2y >= 9,3x+y>= 13, 4x+6y= 24, x <= 5, y <= 5, x>0, y = 0 O Objective Function: Minimize Cost, C-12000x+10000y Constraints: 3x + 2y >= 13, 3x+y>= 9, 4x+6y>= 24, x <= 5, y <= 5, x>= 0, y = 0 O Objective Function: Minimize Cost, C-12000x+10000 Constraints: 3x + 2y > 13, 3x + y 24, 4x+6y>-9, x <= 5, y < 5₁ x >= 0, y = 0 O Objective Function: Minimize Cost, C = 12000x+10000y Constraints: 3x + 2v>= 24 3x+v># 13, 4x+6y>=9₁ x <= 5.v<= 5.x >=0.v> 0

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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**Manufacturing: Production Planning** A mining company owns two different mines that produce ore, which is crushed and graded into three classes: high, medium, and low grade. The company has a contract to provide a smelting plant with at least 13 tons of high-grade, 9 tons of medium-grade, and 24 tons of low-grade ore per week. The two mines have different operating characteristics, as outlined in the table below: | Mine | #Tons/Day High | #Tons/Day Medium | #Tons/Day Low | |-------|----------------|------------------|---------------| | #1 | 3 | 3 | 4 | | #2 | 2 | 1 | 6 | The operating costs for Mine #1 are $12,000 per day and the operating costs for Mine #2 are $10,000 per day. Each mine operates at most 5 days per week. How many days per week should each mine operate to meet or exceed the smelting plant contract and minimize the total cost? Let \( x \) = the number of days per week that Mine 1 operates and Let \( y \) = the number of days per week that Mine 2 operates. Which option (a, b, c, or d) shows the correct objective function and constraints for this application? - a) **Objective Function**: Minimize Cost, C = 12000x + 10000y **Constraints**: \( 3x + 2y \geq 9, 3x + y \geq 13, 4x + 6y \geq 24, x \leq 5, y \leq 5, x \geq 0, y \geq 0 \) - b) **Objective Function**: Minimize Cost, C = 12000x + 10000y **Constraints**: \( 3x + 2y \geq 13, 3x + y \geq 9, 4x + 6y \geq 24, x \leq 5, y \leq 5, x \geq 0, y \geq 0 \) - c) **Objective Function**: Minimize Cost, C = 12000x + 100
Transcribed Image Text:**Manufacturing: Production Planning** A mining company owns two different mines that produce ore, which is crushed and graded into three classes: high, medium, and low grade. The company has a contract to provide a smelting plant with at least 13 tons of high-grade, 9 tons of medium-grade, and 24 tons of low-grade ore per week. The two mines have different operating characteristics, as outlined in the table below: | Mine | #Tons/Day High | #Tons/Day Medium | #Tons/Day Low | |-------|----------------|------------------|---------------| | #1 | 3 | 3 | 4 | | #2 | 2 | 1 | 6 | The operating costs for Mine #1 are $12,000 per day and the operating costs for Mine #2 are $10,000 per day. Each mine operates at most 5 days per week. How many days per week should each mine operate to meet or exceed the smelting plant contract and minimize the total cost? Let \( x \) = the number of days per week that Mine 1 operates and Let \( y \) = the number of days per week that Mine 2 operates. Which option (a, b, c, or d) shows the correct objective function and constraints for this application? - a) **Objective Function**: Minimize Cost, C = 12000x + 10000y **Constraints**: \( 3x + 2y \geq 9, 3x + y \geq 13, 4x + 6y \geq 24, x \leq 5, y \leq 5, x \geq 0, y \geq 0 \) - b) **Objective Function**: Minimize Cost, C = 12000x + 10000y **Constraints**: \( 3x + 2y \geq 13, 3x + y \geq 9, 4x + 6y \geq 24, x \leq 5, y \leq 5, x \geq 0, y \geq 0 \) - c) **Objective Function**: Minimize Cost, C = 12000x + 100
Expert Solution
Step 1
The objective for any linear programming problem including cost is to reduce the cost, if it includes time, the objective becomes to reduce the time, whereas if revenue or profit are involved, the objective becomes to that of maximization. 
 
x and y are number of days per week in Mine 1 and 2 respectively. 
Cost per day is given. Hence, the objective will be to minimize the cost per week. 
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