HW: Solving linear programming problems using Lindo

To be handed in by Jan, 23 ,2001.
  1. Formulate the following problem as an LP, problem, solve it using Lindo:
    A steal factory has capabilities for manufacturing three types of products (1, 2 and 3). Manufacturing of each of the products requires the use of three machines (1, 2 and 3). The maximum time that each of the machines could be operated during the week are (160, 100 and 50) hours respectively. The number of work hours of the machines for each unit of product are:
    Machine 1 for products (1, 2 and 3): 8, 2 and 3 respectively.
    Machine 2 for products (1, 2 and 3): 4, 3 and 0 respectively.
    Machine 3 for products (1, 2 and 3): 2, 0 and 1 respectively.
    The sales department reports that the sales potential of product 1 and 2 is much higher than the manufacturing potential of the factory. In addition, the sales potential of product 3 is limited to 20 units per week.
    The Net profit from a unit of product are (20$, 6$, 8$)
    How much of each product should be manufactured per week?
  2. Solve the following problem graphically (there are only two decision variables). After you solve it, check your solution with Lindo:
    MIN Z = 0.20X1 + 0.08X2
S.T.
X1 <= 80,000
X2 <= 90,000
2X1 - X2 >= 0
X1 + X2 >= 100,000
X1, X2 >= 0
  3. For the problem that was solved in class (see page 10-4), formulate the dual problem and solve it (use Lindo). Explain the connection between the dual problem and the original problem.