A company makes two types of sofas, regular and long, at two locations, one in Nottingham and one in London. The plant in Nottingham has a daily operating budget of £45,000 and can produce at most 300 sofas daily in any combination. It costs £150 to make a regular sofa and £200 to make a long sofa at the Nottingham plant. The London plant has a daily operating budget of £36,000, can produce at most 250 sofas daily in any combination and makes a regular sofa for £135 and a long sofa for £180. The company wants to limit production to a maximum of 250 regular sofas and 350 long sofas each day. If the company makes a profit of £50 on each regular sofa and £70 on each long sofa, how many of each type should be made at each plant in order to maximize profit? What is the maximum profit?

Also demonstrate that the value you obtained as the maximum profit is correct.