A) Solve the following linear program graphically. How many extreme points exist for this problem?
|Min||150X + 210Y|
|s.t.||3.8X + 1.2Y ≥ 22.8|
|Y ≥ 6|
|Y ≤ 15|
|45X + 30Y = 630|
|X, Y ≥ 0|
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 chairs and 4200 chairs, respectively. CPI has a policy of satisfying all 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 produce the seat at a cost of $10.25. CPI can produce up to 3800 seats per quarter.
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 maximum inventory cannot exceed 300 seats.
Formulate this problem as a linear programming problem.