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A furniture manufacturing company plans to make two products. chairs and tables from its available resources, which consists of 400 board feet of mahogany timbers and 450 man-hours of labour. it knows that to make a chair requires 5 board feet and 10 man-hours and yields a profit of 450, while each table uses 20 board feet and 15 man-hours and has a profit of 80.how many chairs and tables should the company make to get the maximum profit under the above resource constraints? Formulate the above as an LPP.

Guest Jan 25, 2015

Best Answer 

 #1
avatar+87301 
+14

We are trying to maximize

P = 450x + 80y

Subject to these  constraint equations:

x ≥ 0,  y ≥ 0,  5x + 20y ≤ 400   and  10x + 15y ≤ 450 ..... where x is the number of chairs produced and y is the number of tables produced

Here's a graph of the feasible region......https://www.desmos.com/calculator/mbousof3x9

The maximum profit occurs at the "corner point".... (24, 14)

So....produce 24 chairs and 14 tables to maximize the profit....

 

CPhill  Jan 25, 2015
 #1
avatar+87301 
+14
Best Answer

We are trying to maximize

P = 450x + 80y

Subject to these  constraint equations:

x ≥ 0,  y ≥ 0,  5x + 20y ≤ 400   and  10x + 15y ≤ 450 ..... where x is the number of chairs produced and y is the number of tables produced

Here's a graph of the feasible region......https://www.desmos.com/calculator/mbousof3x9

The maximum profit occurs at the "corner point".... (24, 14)

So....produce 24 chairs and 14 tables to maximize the profit....

 

CPhill  Jan 25, 2015
 #2
avatar+92777 
+5

 

CPhill's solution is 24 chairs and 14 tables

This gives a profit of

 

$${\mathtt{24}}{\mathtt{\,\times\,}}{\mathtt{450}}{\mathtt{\,\small\textbf+\,}}{\mathtt{14}}{\mathtt{\,\times\,}}{\mathtt{80}} = {\mathtt{11\,920}}$$   dollars

 

I will also check that this fits the limitations.

mahogony = 24*5+14*20=400 good

hours = 24*10+14*15=450  good

--------------------------------------------------------------

My solution is  45 chairs and no tables

This gives a profit of  

 

$${\mathtt{45}}{\mathtt{\,\times\,}}{\mathtt{450}} = {\mathtt{20\,250}}$$   dollars 

 

I will also check that this fits the limitations.

mahogony = 45*5=225 good

hours = 45*10=450  good

 

Here if my graph.   The movable line represents profit.  Basically I just added this to CPhill's graph.

 

Melody's Profit Graph

Melody  Jan 25, 2015
 #3
avatar+87301 
+5

Thanks, Melody....I missed that other corner point.....curses on you !!!! (LOL !!!)

 

I think I just had a.......

 

CPhill  Jan 25, 2015

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