A) Solve the following linear program graphically. How many extreme points exist for this problem? ​...

Question:

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

B)

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.