For the next year, Halmark is planning to expand its greeting card business beyond the East Coast to the Midwest. Jim estimates Halmark's demand for cards in the Midwest. He estimates that the amount of sales (in thousands of tons) that Halmark would make if their price was p (per ton), is equal to ​D(p) = 10-p/40​. The cost of producing one ton of cards is equal to $40.

Note that the demand function and the marginal cost stay the same throughout the problem.

In order to scale up their production to that extent they have three options:

Option 1: Lease for $500,000, a state-of-the-art factory that would allow them to produce 7,000 tons of cards in a year.

a) What is the optimal price and the optimal profit if Hallmark goes with this option?

Option 2: Spend $600,000 on a startup that will not only take care of production and ensure that capacity is unlimited, but also would help them identify all the firms that are willing to pay a price of $300 per ton as well as all the firms who are only willing to pay $150 per ton (but not $300 per ton).

b) What is the profit if Halmark goes with this option (Remember The cost of producing one ton of paper is equal to $40)? 

Option 3: Trust another company to rum production in their farm. Unfortunately, this is a risky option. With probability 70% they can produce unlimited amounts of cards, but with probability 30% there are breakdowns in which case they can only produce 4,000 tons of cards in a year. This option would cost $450,000 for the year.

c) What is the optimal price and the optimal revenue if the production capacity is 4,000 tons?

d) What is their (expected) profit if they go with this option?