A small mining company that produces both copper and nickel owns two mines whose ores contain both minerals. The two mines have different costs and different production rates. Furthermore their products are different. Mine 1 produces 40 tons of copper per day and 15 tons of nickel per day. Mine 2 produces 20 tons of copper/day and 30 tons of nickel/day The company has contracted to provide 100 tons per week of copper and 150 tons per week of nickel. Daily operating costs have been estimated as $3,000 and $9,000 for mines 1 and 2, respectively. The company policy states that neither mine can be in operation for more than 5 days per week for safety reasons. The company is interested to identify number of days per week mines 1 and/or 2 should be operated so that the company meet its contract obligation at least total cost. Answer the following questions based on the information provided.

a) Formulate the problem mathematically

b) Solve this linear optimization problem using graphical method (show the graph and lightly shade in the feasible region if there is one)

* PLEASE PROVIDE HAND CALCULATION, NO MATLAB

Question-4 (LP problem) A small mining company that produces both copper and nickel owns two mines whose ores contain both minerals. The two mines have different costs and different production rates. Furthermore their products are different. Mine 1 produces 40 tons of copper per day and 15 tons of nickel per day. Mine 2 produces 20 tons of copper/day and 30 tons of nickel/day The company has contracted to provide 100 tons per week of copper and 150 tons per week of nickel. Daily operating costs have been estimated as $3,000 and $9,000 for mines 1 and 2, respectively. The company policy states that neither mine can be in operation for more than 5 days per week for safety reasons. The company is interested to identify number of days per week mines 1 and/or 2 should be operated so that the company meet its contract obligation at least total cost. Answer the following questions based on the information provided. a) Formulate the problem mathematically b) Solve this linear optimization problem using graphical method (show the graph and lightly shade in the feasible region if there is one) Question-4 (LP problem) A small mining company that produces both copper and nickel owns two mines whose ores contain both minerals. The two mines have different costs and different production rates. Furthermore their products are different. Mine 1 produces 40 tons of copper per day and 15 tons of nickel per day. Mine 2 produces 20 tons of copper/day and 30 tons of nickel/day The company has contracted to provide 100 tons per week of copper and 150 tons per week of nickel. Daily operating costs have been estimated as $3,000 and $9,000 for mines 1 and 2, respectively. The company policy states that neither mine can be in operation for more than 5 days per week for safety reasons. The company is interested to identify number of days per week mines 1 and/or 2 should be operated so that the company meet its contract obligation at least total cost. Answer the following questions based on the information provided. a) Formulate the problem mathematically b) Solve this linear optimization problem using graphical method (show the graph and lightly shade in the feasible region if there is one)