Problem C (35 points / 5 points for each
question)
Lafayette Corp. manufactures aluminum patio furniture. There are
four different pieces in a new design line of furniture. A Linear
Programming model has been developed (see the given program
solution output) to determine the number of each piece to produce
this week. The four variables (CH, DT, LG, ET) represent,
respectively, the number of chairs, dining tables, lounges, and end
tables to be produced. The objective function measures the total
profit (assume all units produced will be sold). The first three
constraints, respectively, measure the aluminum (in pounds), the
amount of fabrication time (in hours), and the amount of finishing
time (in hours) required for production. The fourth and the fifth
constraints are marketing restrictions. The sixth and seventh
constraints specify relative production levels.
Linear Program listed:
Maximize 18CH+24DT+45LG+18ET
Subject to
Const1) 6CH+18DT+15LG+4ET<=2700
Const2) 0.4CH+0.3DT+0.6LG+0.4ET<=200
Const3) 0.2CH+0.16DT+0.25LG+0.12ET<=110
Const4) DT>=30
Const5) LG <=60
Const6) CH-6DT>=0
Const7) -LG+2ET<=0
Program Solution Output listed:
OBJECTIVE FUNCTION VALUE 7380.000
VARIABLE VALUE REDUCED COST
CH 190.000000 0.000000
DT 30.000000 0.000000
LG 60.000000 0.000000
ET 30.000000 0.000000
ROW SLACK OR SURPLUS SHADOW(DUAL) PRICES
Const1) 0.000000 3.000000
Const2) 67.000000 0.000000
Const3) 48.599998 0.000000
Const4) 0.000000 -30.000000
Const5) 0.000000 3.000000
Const6) XXX 0.000000
Const7) 0.000000 3.000000
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJECTIVE FUNCTION COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE COEF INCREASE ALLOWABLE COEF
DECREASE
CH 18.000000 1.058824 10.000000
DT 24.000000 30.000000 INFINITY
LG 45.000000 INFINITY 3.000000
ET 18.000000 INFINITY 6.000000
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE RHS INCREASE ALLOWABLE RHS
DECREASE
Const1 2700.000000 1004.999939 60.000000
Const2 200.000000 INFINITY 67.000000
Const3 110.000000 INFINITY 48.599998
Const4 30.000000 1.111111 30.000000
Const5 60.000000 3.529412 60.000000
Const6 0.000000 10.000000 INFINITY
Const7 0.000000 30.000000 60.000000
Use the above given outputs to answer the following questions.
There is no need to run the program with any software. The above
given output contains all the needed analysis information.
(C-1) How much total time will be actually used in the
fabrication area?
(C-2) What is the optimal arrangement for the production of
these four pieces of furniture?
(C-3) How much profit can be generated by all the produced
dining tables?
(C-4) If someone offers you 20 pounds of aluminum for the price
of $55, will you accept the offer? Why or why not?
(C-5) What is the required finishing time to produce a dining
table?
(C-6) If the newly adjusted unit profit for a chair is now $15,
what will be the adjusted total profit?
(C-7) The SLACK or SURPLUS information for constraint 6 (line
Const6) is missing and currently shown as “XXXâ€. What is the actual
value of “XXX� Is this a slack or a surplus outcome? Explain.