Unit processing times (in hrs) Product 1 Product 2 Minimum Working Hours Plant 1 2 4 16 Plant 2 4 3 24 Unit production costs 6. 3
Suppose that you have two products, (Product 1 and 2), which can be produced in one of two plants (Plant 1 and 2). The corresponding unit processing times of each product on each plant, and their unit costs are given. Each plant has a minimum working hour limit, as shown in the table below.
Decision variables for the problem are defined as x: number of product 1 produced, and y:number of product 2 produced. Formulated the problem as an LP minimizing total cost and solve it by graphical method. Explicitly show the isocost lines, the intersection of the costraints and the optimal solution on the graph.
Then, according to your graph, answer the following questions.
(a) What is the shadow price of the Constraint 1(Plant 1 Constraint)? Compute and show on graph.
(b) What is the shadow price of the Constraint 2(Plant2 Constraint)? Compute and show on graph.
(c) What is the reduced cost of x? (How much should the objective function coefficient of x reduced from 6 for it to become nonzero in the optimal solution?)
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