Last week you were asked to formulate this linear program.  The formulation with explanation is as follows.  The LINDO output is also included.  Answer the six questions.   

 

Comfort Plus Inc. (CPI) manufactures a standard dining chair used in restaurants.  The demand forecasts for quarter 1 (January - March) and quarter 2 (April - June) are 3700 and 4200 chairs, respectively.  CPI has a policy of satisfying demand in the quarter in which it occurs. 

 

The chair contains an upholstered seat that can be produced by CPI or purchased from DAP, a subcontractor.  DAP currently charges $12.50 per seat, but has announced a new price of $13.75 effective April 1.  CPI can produced 3800 seats per quarter at a cost of $10.25 per seat. 

 

Seats that are produced or purchased in quarter 1 and used to satisfy demand in quarter 2 cost CPI $1.50 each to hold in inventory, but the maximum inventory cannot exceed 300 seats. 

 

CPI1 = number of seats produced by CPI in quarter 1 

DAP1 = number of seats purchased from DAP in quarter 1 

 

INV = number of seats carried in inventory from quarter 1 to quarter 2 

 

CPI2 = number of seats produced by CPI in quarter 2 

 

DAP2 = number of seats purchased from DAP in quarter 2 

 

 

 

 

 

LP 

 

minÂ	10.25CPI1Â	+ 12.5DAP1Â	+ 1.5INVÂ	+ 10.25CPI2 Â	+ 13.75DAP2Â	Â	Â
s.t.Â	CPI1Â	+ DAP1Â	- INVÂ	Â	Â	>Â	3700Â
Â	Â	Â	INVÂ	+ CPI2Â	+ DAP2Â	>Â	4200Â
Â	CPI1Â	Â	Â	Â	Â	<Â	3800Â
Â	Â	Â	Â	CPI2Â	Â	<Â	3800Â
Â	Â	Â	INVÂ	Â	Â	<Â	300Â
Â	Â	Â	CPI1, CPI2, DAP1, DAP2, INVÂ			>Â	0Â
Â	Â	Â	Â	Â	Â	Â	Â

 

 

 

 

 

 

 

LP OPTIMUM FOUND AT STEP      4 

 

 

 

        OBJECTIVE FUNCTION VALUE 

 

 

 

        1)      82175.00 

 

 

 

  VARIABLE        VALUE          REDUCED COST 

 

      CPI1      3800.000000          0.000000 

 

      DAP1         0.000000          0.250000 

 

       INV       100.000000          0.000000 

 

      CPI2      3800.000000          0.000000 

 

      DAP2       300.000000          0.000000 

 

 

 

 

 

       ROW   SLACK OR SURPLUS     DUAL PRICES 

 

        2)         0.000000        -12.250000 

 

        3)         0.000000        -13.750000 

 

        4)         0.000000          2.000000 

 

        5)         0.000000          3.500000 

 

        6)       200.000000          0.000000 

 

 

 

 NO. ITERATIONS=       4 

 

 

 

 

 

 RANGES IN WHICH THE BASIS IS UNCHANGED: 

 

 

 

                           OBJ COEFFICIENT RANGES 

 

 VARIABLE         CURRENT        ALLOWABLE        ALLOWABLE 

 

                   COEF          INCREASE         DECREASE 

 

     CPI1       10.250000         2.000000         INFINITY 

 

     DAP1       12.500000         INFINITY         0.250000 

      INV        1.500000         2.000000         0.250000 

     CPI2       10.250000         3.500000         INFINITY 

     DAP2       13.750000         0.250000         2.000000 

 

                           RIGHTHAND SIDE RANGES 

      ROW         CURRENT        ALLOWABLE        ALLOWABLE 

                    RHS          INCREASE         DECREASE 

        2     3700.000000       100.000000       200.000000 

        3     4200.000000         INFINITY       300.000000 

        4     3800.000000       200.000000       100.000000 

        5     3800.000000       300.000000      3800.000000 

        6      300.000000         INFINITY       200.000000 

 

 

 

To receive full credit You should be able to justify your answer based on the output alone without resolving the linear program.   

 

1. What is the optimal solution including the optimal value of the objective function?

 

 

1. If the per-unit inventory cost increased from $1.50 to $2.50, would the optimal solution change?  Would the optimal value of the objective function change?

 

1. If in quarter 2 CPI's per-seat production cost increased by $1.25 and DAP changed its mind about the announced price increase (thus leaving it at $12.50 per seat), would the optimal solution change?

 

1. If DAP reduced its per seat selling price in quarter 1 from $12.50 to $12.30, should CPI purchase any seats in quarter 1?

 

1. How much is it worth to CPI to increase its inventory capacity from 300 to 400?

 

1. If CPI increased its production capacity by 100 seats in both quarters 1 and 2, what would be the savings for CPI (ignoring the capacity expansion expense)?