one Q for operation research



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.

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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.

Formulate a linear program to help minimize cost while satisfying demand.  Solve the LP using Solver or LINDO and generate the range sensitivity analysis as part of the output.