Solve this problem using the simplex method.

A company makes two types of sofas, regular and long, at two locations, one in Hickory and one in Lenoir.

The plant in Hickory has a daily operating budget of $63000 and can produce at most 420 sofas daily in any combination. It costs $150 to make a regular sofa and $200 to make a long sofa at the Hickory plant. The Lenoir plant has a daily operating budget of $50400, can produce at most 350 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 350 regular sofas and 490 long sofas each day.

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?

Write all of the constraints and the profit function using the following variable names:

x1= # regular sofas made at Hickory x2= # long sofas made at Hickory x3= # regular sofas made at Lenoir x4= # long sofas made at Lenoir 

(a) You will now be asked to give some of your constraints. (Note that there are more constraints than the ones specifically asked for.) Do not include any "$" symbols or commas in your constraints or they will be graded as incorrect.(b) Solve the problem using the simplex method and answer the following questions. Do not use commas in your answers or they will be graded as incorrect.

In the optimal solution, how many regular sofas are produced?

In the optimal solution, how many long sofas are produced?

In the optimal solution, how many long sofas are produced in Hickory?

In the optimal solution, how many regular sofas are produced in Lenoir?

What is the maximum profit?

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