Problem 2: A small manufacturer has two plants located in New York and Ohio. It is possible to produce any of the three products A, B, and C at either of the two plants. The profit from products A, B, and C is expected to be $35, $45, and $55 per unit respectively. Products A, B and C require 2.0, 3.5 and 4.0 hours of labor respectively. Similarly, these products require 1.5, 2.9, and 3.4 hours of machine time respectively. In New York the firm has 1800 hours of labor and 2000 hours of machine time available next month. In Ohio, the capacities are 4000 hours of labor and 4000 hours of machine time. The sales department estimates that the maximum monthly sales of each product can be 500, 700, and 400 units respectively. The human resource department wants to be sure that the same proportion of labor hours be used at each plant. Solve this linear programming problem to determine the production plan, which will maximize the profit. (Hint: 6 variables and 8 constraints)

1. Formulate the Linear Programming model (Define one decision variable completely and list the symbols for others, Write the objective function and list all the constraints)

1. Solve the problem using Excel Solver or POM/QM. Show below the value of each decision variable and the objective function.