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 $36000 and can produce at most 240 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 $28800, can produce at most 200 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 200 regular sofas and 280 long sofas each day. The company makes a profit of $35 on each regular sofa and $49 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.Give the constraint that indicates the limit on sofa production at the Lenoir plant. x3+x4<=200 Give the constraint that indicates the budget limit at the Hickory plant. 150x1+200x2<=36000 Give the constraint that states the limit on long sofas produced. x2+x4<=280

(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? 80 In the optimal solution, how many long sofas are produced? 280 In the optimal solution, how many long sofas are produced in Hickory? 120 In the optimal solution, how many regular sofas are produced in Lenoir? 100 What is the maximum profit? $229.83