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

Question

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.

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

A)What would the maximum possible profit be?

B)How many house 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?

Explanation / Answer

Let X = tables to be produce .

Y = chairs to be produce .

Maximize possible profit = 80 X + 50 Y

Solution equations are,

3 X + 3 Y ? 360

4 X + 2Y ? 240

X and Y ? 0 & integer.

given that X = 0 and Y = 120 for optimal ,

a) then Maximize possible profit = 80 X + 50 Y

= 80(0) + 50 (120)

=6000

b) Maximize profit means , x =0 and y=120

then we consider only chairs .

$50 of profit requires 3hours of assembly time .

then $6000 of maximum profit requires =(6000/50) * 3 = 360

c) if a new constraint , 2x+2y <400 added ,

then

x +y < 200

maximum possible profit would not change because this constraint also

met under already given constraints .

as per given , x =0 and y =120,

this is also meeting the given constraint , x + y <200

so there would be no change in maximal profit

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