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 4500 and 55000 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 $12.00 per seat, but has announced a new price of $13.50 effective April 1. CPI can produced 4700 seats per quarter at a cost of $11.00 per seat. Seats that are produced or purchased in quarter 1 and used to satisfy demand in quarter 2 cost CPI $2.50 each to hold in inventory, but the maximum inventory cannot exceed 400 seats. Formulate a linear program to help minimize cost while satisfying demand.

a. What is the optimal production plan and what will it cost?

b. If the per-unit inventory cost increased from $2.50 to $3.50, based on the sensitivity analysis provided would the optimal production plan change? If necessary, revise and resolve the linear program with either SOLVER or LINDO. What is the new production plan and cost?

c. If in quarter 2, DAP decided to increase the price by an additional $0.50 (to $14.00 instead of $13.50) would the production plan change? Would the total cost change?