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.
+128407 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....
+128407 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....
+118608
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
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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.
