The ABC Manufacturing Company makes two products. The profit estimates are $5 for each unit of product 1 sold and $4 for each unit of product 2 sold. The labor-hour requirements for the products in each of three production departments are summarized below:

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labor-hour requirements(hrs) labor-hour product 1 product 2 availability Department A 1.50 3.00 450Department B 2.00 1.00 350Department C 1.00 1.00 200

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Assuming that the company is interested in maximizing profits, the following LP formulation and LINDO computer output are given:Let X1 = units of product 1 X2 = units of product 2 MAX 5 X1 + 4 X2 SUBJECT TO 2) 2.0 X1 + 1.0 X2 <= 350 3) 1.5 X1 + 3.0 X2 <= 450 4) 1.0 X1 + 1.0 X2 <= 200 END LP OPTIMUM FOUND AT STEP 1 OBJECTIVE FUNCTION VALUE 1) 950.00000 VARIABLE VALUE REDUCED COST X1 150.000000 .000000 X2 50.000000 .000000 ROW SLACK OR SURPLUS DUAL PRICES 2) .000000 1.000000 3) 75.000000 0.000000 4) .000000 3.000000 NO. ITERATIONS= 1

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Based on the above computer output, answer the following questions.

(a) How many units of each product should be produced in order to maximize the profit contribution? What is the projected profit?

(b) What are the required labor hours in each department for the above production and the slack hours in each department?

(c) This company is going to hire a new full-time employee and assign this person to Department B to increase production. Do you think this decision can help this company? Explain why or why not to justify your answer.

(d) Formulate the dual form of the above problem.

(e) Find the dual optimal solution, including the optimal objective function value and the optimal value of all the dual variables.