(1) Find the maximum value of *z* = 5*x* – 2*y* subject to the constraints *x* + *y* ≥ 2

2*x* + 3*y* ≤ 12

3*x* + 2*y* ≤ 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?