A furniture company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of hours of carpentry work, a certain number of labor hours in the painting and varnishing department, and a certain number of labor hours in the inspection department. The production requirements, profits, and daily man-hour availability are as follows:

Hours required to

produce one unit Available

------------------------- hours/day

Department Tables Chairs

----------------------------------------------------------------

Carpentry 3 2 300

Painting/varnishing 3 4 240

Inspection 2 1 100

----------------------------------------------------------------

Profit ($/unit) 4 3

Using the following decision variables

X1 = the number of units of tables to be produced

X2 = the number of units of chairs to be produced

the following computer output is obtained by LINDO:

MAX 4 X1 + 3 X2

SUBJECT TO

2) 3 X1 + 2 X2 <= 300

3) 3 X1 + 4 X2 <= 240

4) 2 X1 + X2 <= 100

END

LP OPTIMUM FOUND AT STEP 2

OBJECTIVE FUNCTION VALUE

1) 236.000000

VARIABLE VALUE REDUCED COST

X1 32.000000 .000000

X2 36.000000 .000000

ROW SLACK OR SURPLUS DUAL PRICES

2) 132.000000 .000000

3) 0.000000 0.400000

4) 0.000000 1.400000

NO. ITERATIONS= 2

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Answer the following questions based on the above computer output with the formulation given.

(1) How many units of each product should be produced in order to maximize the profit contribution? And what is the total profit from this production? (3 points)

(2) How many hours are required in each department for the above optimal production to maximize the profit? Also, find the slack hours in each department. (4 points)

(3) This company is going to hire a new full-time employee and assign this person to the first department of carpentry work. Do you think this decision is right? Explain why or why not to justify your answer. (3 points)

(4) Formulate the dual form of the above problem. (4 points)

5. Find the dual optimal solution, including the optimal objective function value and the optimal value of all the dual variables. (4 points)