a company makes a single product on two separate production lines, a

  

(1) Find the maximum value of z = 5x – 2y subject to the constraints
x + y ≥ 2
2x + 3y ≤ 12
3x + 2y ≤ 12
x ≥ 0, y ≥ 0

(2) Set up the objective function and constraints and then solve for the following:
A company makes a single product on two separate production lines, A and B. The company’s labor force is equivalent to 1,000 hours per week, and it has $3,000 outlay weekly for operating costs. It takes 1 hour and 4 hours to produce a single item on lines A and B, respectively. The cost of producing a single item on A is $5 and on B is $4. How many items should be produced on each line to maximize the total output?

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