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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 fe

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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.

Jan 25, 2015

#1
+96067
+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....

Jan 25, 2015

#1
+96067
+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
#2
+97555
+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

Jan 25, 2015
#3
+96067
+5

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

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

Jan 25, 2015