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You are an engineer at a mining company which sells a mineral ore in three qu
You are an engineer at a mining company which sells a mineral ore in three quality grades: Low, Medium, and High. The company owns three mines which produce this ore: Mine A, Mine B, and Mine C. Each mine can produce different quantities (in tons) of each grade of ore per day as shown below:
Where xy are the last two digits of your URN. For example, for the URN 6835725, xy = 25. In this case Mine A produces 60+25 = 85 tons of Low-quality ore per day. Please write your value of xy at the top of your solution. The company has a contract to deliver 800 tons of Low-quality ore, 900 tons of Medium-quality ore, and 1000 tons of High-quality ore. The set of equations which relates the number of days (a, b, c) each mine (A, B, C) must operate to the produce required quantities of ore is: (60 + ????????)???? + 15???? + 10???? = 800 70???? + 10???? + (30 + ????????)???? = 900 20???? + 50???? + 35???? = 1000
a) (i) Write the system of equations in matrix form
(ii) Using matrix methods, solve for the number of days each mine must operate to meet this contract with no excess ore (fractions of a day are ok).
b) If one mine is not available, discuss the mathematical implications for computing the number of days the remaining mines must operate (you do not need to solve). Also, discuss the consequences for the quantity of ore produced to meet the contract
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