Susanna Nanna is the production manager for a furniture manufacturing company. The company produces ...

Susanna Nanna is the production manager for a furniture manufacturing company. The company produces tables (X) and chairs (Y). Each table generates a profit of $80 and requires 3 hours of assembly time and 4 hours of finishing time. Each chair generates $50 of profit and requires 3 hours of assembly time and 2 hours of finishing time. There are 360 hours of assembly time and 240 hours of finishing time available each month. The following linear programming problem represents this situation.

Maximize    80X + 50Y
Subject to:    3X + 3Y ≤ 360
   4X + 2Y ≤ 240
   X, Y ≥ 0

The optimal solution is X = 0, and Y = 120.

(a) What would the maximum possible profit be?
(b) How many hours of assembly time would be used to maximize profit?
(c) If a new constraint, 2X + 2Y ≤ 400, were added, what would happen to the maximum possible profit?