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A mining company owns 3 different mines (North, South, and West mines) that produce 3 different grades of iron (low-grade, medium-grade, and high-grade). The company requires at least 25 tons of low-grade iron, 18 tons of medium-grade iron, and 12 tons of high-grade iron in order to meet its supply requirements. The North Mine costs $10,000 per day of mining and in a day of mining it produces 4 tons of low-grade iron, 1 ton of medium-grade iron, and 1 ton of high-grade iron. The South Mine costs $15,000 per day of mining and in a day of mining it produces 1 ton of low-grade iron, 3 tons of medium grade iron, and 2 tons of high-grade iron. The West Mine costs $18,000 per day of mining and in a day of mining it produces 3 tons of low-grade iron, 3 tons of medium-grade iron, and no high-grade iron. Suppose x is the number of days that the North Mine is operational, y is the number of days that the South Mine is operational, and z is the number of days that the West Mine is operational. If the company wants to minimize its total cost while satisfying its supply requirements, fill in the blanks below to formulate this situation as a linear program. (Make sure to input only numbers, do not include any dollar signs, commas, periods, or other symbols in your answers)

A mining company owns 3 different mines (North, South, and West mines) that produce 3 different grades of iron (low-grade, medium-grade, and high-grade). The company requires at least 25 tons of low-grade iron, 18 tons of medium-grade iron, and 12 tons of high-grade iron in order to meet its supply requirements. The North Mine costs $10,000 per day of mining and in a day of mining it produces 4 tons of low-grade iron, 1 ton of medium-grade iron, and 1 ton of high-grade iron. The South Mine costs $15,000 per day of mining and in a day of mining it produces 1 ton of low-grade iron, 3 tons of medium grade iron, and 2 tons of high-grade iron. The West Mine costs $18,000 per day of mining and in a day of mining it produces 3 tons of low-grade iron, 3 tons of medium-grade iron, and no high-grade iron. Suppose x is the number of days that the North Mine is operational, y is the number of days that the South Mine is operational, and z is the number of days that the West Mine is operational. If the company wants to minimize its total cost while satisfying its supply requirements, fill in the blanks below to formulate this situation as a linear program. (Make sure to input only numbers, do not include any dollar signs, commas, periods, or other symbols in your answers)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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QUESTION 12 A mining company owns 3 different mines (North, South, and West mines) that produce 3 different grades of iron (low-grade, medium-grade, and high-grade). The company requires at least 25 tons of low-grade iron, 18 tons of medium-grade iron, and 12 tons of high-grade iron in order to meet its supply requirements. The North Mine costs $10,000 per day of mining and in a day of mining it produces 4 tons of low-grade iron, 1 ton of medium-grade iron, and 1 ton of high-grade iron. The South Mine costs $15,000 per day of mining and in a day of mining it produces 1 ton of low-grade iron, 3 tons of medium grade iron, and 2 tons of high-grade iron. The West Mine costs $18,000 per day of mining and in a day of mining it produces 3 tons of low-grade iron, 3 tons of medium-grade iron, and no high-grade iron. Suppose x is the number of days that the North Mine is operational, y is the number of days that the South Mine is operational, and z is the number of days that the West Mine is operational. If the company wants to minimize its total cost while satisfying its supply requirements, fill in the blanks below to formulate this situation as a linear program. (Make sure to input only numbers, do not include any dollar signs, commas, periods, or other symbols in your answers) Minimize X + y+ Z Subject to: x + y+ z ≥ 25 X+ y + z≥ 18 x+ I y+ Z≥ 12 x 2 y2 ZZ For Blank 11
Transcribed Image Text:QUESTION 12 A mining company owns 3 different mines (North, South, and West mines) that produce 3 different grades of iron (low-grade, medium-grade, and high-grade). The company requires at least 25 tons of low-grade iron, 18 tons of medium-grade iron, and 12 tons of high-grade iron in order to meet its supply requirements. The North Mine costs $10,000 per day of mining and in a day of mining it produces 4 tons of low-grade iron, 1 ton of medium-grade iron, and 1 ton of high-grade iron. The South Mine costs $15,000 per day of mining and in a day of mining it produces 1 ton of low-grade iron, 3 tons of medium grade iron, and 2 tons of high-grade iron. The West Mine costs $18,000 per day of mining and in a day of mining it produces 3 tons of low-grade iron, 3 tons of medium-grade iron, and no high-grade iron. Suppose x is the number of days that the North Mine is operational, y is the number of days that the South Mine is operational, and z is the number of days that the West Mine is operational. If the company wants to minimize its total cost while satisfying its supply requirements, fill in the blanks below to formulate this situation as a linear program. (Make sure to input only numbers, do not include any dollar signs, commas, periods, or other symbols in your answers) Minimize X + y+ Z Subject to: x + y+ z ≥ 25 X+ y + z≥ 18 x+ I y+ Z≥ 12 x 2 y2 ZZ For Blank 11
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