I'm having a test tomorrow on linear programming. My teacher posted the sample test today but there's no answers. I solved that by comparing answers with my friends though (:. But I need help solving this problem that we can't seem to figure out. Thanks in advance!

A company makes 2 types of sofas, regular and long, at 2 locations, one in Hampton and one in Lakeside. The plant in Hampton 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 Hampton plant. The Lakeside 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 for each regular sofa and $70 for each long sofa, how many of each type should be made at each plant in order to maximize profit? What is the maximum profit?

As your class implies; linear programming. This requires you to get multiple equations (i.e.
constant*[unknown_1] + constant*[unknown_2] + ... + constant*[unkown_n] = solution_1
constant*[unknown_1] + constant*[unknown_2] + ... + constant*[unkown_n] = solution_2
constant*[unknown_1] + constant*[unknown_2] + ... + constant*[unkown_n] = solution_3 )

It's always important to first realize your unknowns, since this is what you will be solving for. In this case the unknowns are the two types of sofas, but from two different places. This means you have 4 unknowns. Now the amounts of each relate to the constants. So, write up the equations for me =).

The constants can be anything as long as they relate in the solution. Such as amount*unkown_1 + amount*unknown_2 = total amount. Or cost*unknown_1 + cost*unknown_2 = total_cost etc.

Once you get all your equations you can use a calculator to rref (reduced row echelon form) the matrix, or do your elimination of variables, or do substitutions.