Derive the profit-maximizing quantity

[banixd]

Hello guys, i wanted to ask if someone could help me withone excecise that I not really understand. Im new in Business Math and would be thankfull for an answer.
This is not a Homework but something similar could be in the exam. Thank you

The excercise is:

• Suppose an electricity company owns a power-plant with attached coal mine. The plant needs 1 ton of coal to produce 1 giga-watt of electricity. Currently, the plant and its attached mine are closed. Located in proximity to the power plant’s location, a single potential customer, an aluminum company, is believed to pay up to € 2 per giga-watt electricity and to buy exactly 10 giga-watts during one upcoming production year. Reactivating the power plant and coal mine, the electricity company incurs set-up costs of € 10. Once being set up, the mine has a capacity of 20 tons of coal per year. Labor costs in mining add € 0.8 per ton of coal produced.
• 
  
• a) Is it profitable for the electricity company to reactivate the power plant and its attached coal mine for this one customer only? Derive the profit-maximizing quantity of coal to be mined and the span of prices which can be charged to the customer, the aluminum company, without making losses.
• b) Provide your arguments and illustrate graphically that the electricity company cannot implement the optimal solution (derived in part a) above) by internally communicating a price for one gigawatt of electricity if production managers maximize their plant’s surplus.

 

[Romsek]

I don't see how this can be answered effectively without knowing something about the disposition of the coal in excess of 10 tons.

If any excess is just to be discarded obviously you only want to mine as much as the customer needs. There's nothing to maximize.
If excess can be sold we need to know at what price.

 

[banixd]

I don't see how this can be answered effectively without knowing something about the disposition of the coal in excess of 10 tons.

If any excess is just to be discarded obviously you only want to mine as much as the customer needs. There's nothing to maximize.
If excess can be sold we need to know at what price.

Exactly thats what im confused too. But belive it or not exactly this excercise was on the last exam and im wondering if something similar comes like this i have no clue what to do