Susanna Nanna Is the Production Manager for a Furniture Manufacturing

Essay

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?