A furniture firm manufactures chairs and tables, each requiring the use of three machines A, B and C. Production of each chair requires 2 hours on machine A, 1 hour on machine B and 1 hour on machine C. Each table requires 1 hour each on machine A and B and 3 hours on machine C. The profit obtained by selling one chair is Rs. 30 while by selling one table the profit is Rs. 60. The total time available per week on machine A is 70 hours, on machine B is 40 hours and on machine C is 90 hours. How many chairs and tables should be made per week so as to maximise profit? Formulate the problem as LPP and solve it graphically.
Answers
Maximum Profit , 25 Tables , 15 Chairs = 1950 , A Hrs = 55 , B hrs = 40 hrs , C hrs = 90 Hrs
Step-by-step explanation:
Ch = 2A + B + C
T = A + B + 3C
Profit = 30 * Ch + 60T
A ≤ 70 A = 2*Ch + T
B ≤ 40 B = Ch + T
C ≤ 90 C = Ch + 3T
B ≤ 40 and Each chair & Table need 1 Hour
=> Chair + Tables ≤ 40
C = 90 hrs => max number of Tables = 90/3 = 30
Profit is more on Tables . So we will start with maximum tables
Table Chair A B C Profit
30 0 30 30 90 1800
29 3 35 32 90 1830
28 6 40 34 90 1860
27 9 45 36 90 1890
26 12 50 38 90 1920
25 15 55 40 90 1950
24 16 56 40 88 1920
23 17 57 40 86 1890
22 18 58 40 84 1860
Maximum Profit
25 Tables , 15 Chairs = 1950
A Hrs = 55 , B hrs = 40 hrs , C hrs = 90 Hrs
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