4.1 (due Nov. 19) The United Coal Company owns n coal mines and m coal power plants. You have the following information: For each i [n] you have: - C; = the cost in USD) to mine a metric ton of coal in the 2-th mine, - Li = maximum amount (in metric tons) of coal that can be mined in the i-th mine in a day. . For each i [n] and each j [m] you have: Tij = the cost (in USD) to transport a metric ton of coal from the 2-th mine to the j-th power plant. For each j e [m] you have - P = amount of electricity (in MWh) produced by burning a metric ton of coal in the j-th power plant (each plant has different efficiency); - M = amount of mercury (in grams) released by burning a metric ton of coal in the j-th power plant (each plant has a different pollution control system). Q = price of electricity (in USD per MWh). W = EPA limit on mercury emissions (in grams per MWh). You want to make as much money as possible. You need to comply with the EPA limitthat means if United Coal Company (aggregated over all power plants it owns) produces MWh of electricity per day then United Coal Company can release (aggregated over all power plants it owns) at most W. I grams of mercury per day. Write a linear program that determines how much profit you can make each day (profit = price of electricity produced minus costs in this problem we have mining costs and transportation costs)). Clearly state what are the variables in your linear program and what is their meaning. 4.1 (due Nov. 19) The United Coal Company owns n coal mines and m coal power plants. You have the following information: For each i [n] you have: - C; = the cost in USD) to mine a metric ton of coal in the 2-th mine, - Li = maximum amount (in metric tons) of coal that can be mined in the i-th mine in a day. . For each i [n] and each j [m] you have: Tij = the cost (in USD) to transport a metric ton of coal from the 2-th mine to the j-th power plant. For each j e [m] you have - P = amount of electricity (in MWh) produced by burning a metric ton of coal in the j-th power plant (each plant has different efficiency); - M = amount of mercury (in grams) released by burning a metric ton of coal in the j-th power plant (each plant has a different pollution control system). Q = price of electricity (in USD per MWh). W = EPA limit on mercury emissions (in grams per MWh). You want to make as much money as possible. You need to comply with the EPA limitthat means if United Coal Company (aggregated over all power plants it owns) produces MWh of electricity per day then United Coal Company can release (aggregated over all power plants it owns) at most W. I grams of mercury per day. Write a linear program that determines how much profit you can make each day (profit = price of electricity produced minus costs in this problem we have mining costs and transportation costs)). Clearly state what are the variables in your linear program and what is their meaning