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

#1**+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**+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**+5 ****Melody's Profit Graph**

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
Jan 25, 2015