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a company manufactures two products x1 and x2 on three machines a, b, and c. X1 requires 1 hour on machine A and 1 hour on machine B and yields a revenue of Rs.3/-. Product X2 requires 2 hours on machine A and 1 hour on machine B and 1 hour on machine C and yields revenue of Rs.5/-. In the coming planning period the available time of three machines A, B, C are 2000 hours, 1500 hours, and 600 hours respectively. Find the optimal product mix.

a company manufactures two products x1 and x2 on three machines a, b, and c. X1 requires 1 hour on machine A and 1 hour on machine B and yields a revenue of Rs.3/-. Product X2 requires 2 hours on machine A and 1 hour on machine B and 1 hour on machine C and yields revenue of Rs.5/-. In the coming planning period the available time of three machines A, B, C are 2000 hours, 1500 hours, and 600 hours respectively. Find the optimal product mix.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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a company manufactures two products x1 and x2 on three machines a, b, and c. X1 requires 1 hour on machine A and 1 hour on machine B and yields a revenue of Rs.3/-. Product X2 requires 2 hours on machine A and 1 hour on machine B and 1 hour on machine C and yields revenue of Rs.5/-. In the coming planning period the available time of three machines A, B, C are 2000 hours, 1500 hours, and 600 hours respectively. Find the optimal product mix.

10:08 .l *4 26) $4G QUESTIONS 1. An aviation fuel manufacturer sells two types of fuel A and B. Type A fuel is 25 % grade 1 gasoline, 25 % of grade 2 gasoline and 50 % of grade 3 gasoline. Type B fuel is 50 % of grade 2 gasoline and 50 % of grade 3 gasoline. Available for production are 500 liters per hour grade 1 and 200 liters per hour of grade 2 and grade 3 each. Costs are 60 paise per liter for grade 1, 120 paise for grade 2 and100 paise for grade 3. Type A can be sold at Rs. 7.50 per liter and B can be sold at Rs. 9.00 per liter. How much of each fuel should be made and sold to maximise the profit. 2. A company manufactures two products X, and X, on three machines A, B, and C. X, require I hour on machine A and 1 hour on machine B and yields a revenue of Rs.3/-. Product X, requires 2 hours on machine A and 1 hour on machine B and 1 hour on machine Cand yields revenue of Rs. 5/-. In the coming planning period the available time of three machines A, B, and C are 2000 hours, 1500 hours and 600 hours respectively. Find the optimal product mix. 3. Maximize Z = 1 x+1 y S.T. 1x + 2 y < 2000 1x +1y s 1500 0 x +1 y s 600 and both x and y are > 0. 4. Maximise Z = 8000a + 7000b S.T. За+1bs 66 l a + 1 b < 45 1 a + 0b < 20 0 a + 1 b s 40 and both a and b are 2 0. 5. Minimise Z = 1.5 x + 2.5 y S.T. 1 x+ 3 y > 3 1x + 6 y 2 2 and both x and y > 0 6. Maximise Z= 3 a + 2 b S.T. la - 1 b s 1 l a + lb 2 3 and both x and y are 0 7. Maximise Z= -3 x + 2 y S.T. 1x +0 y s 3 1x -ly s 0 and both x and y are > 0 |||
Transcribed Image Text:10:08 .l *4 26) $4G QUESTIONS 1. An aviation fuel manufacturer sells two types of fuel A and B. Type A fuel is 25 % grade 1 gasoline, 25 % of grade 2 gasoline and 50 % of grade 3 gasoline. Type B fuel is 50 % of grade 2 gasoline and 50 % of grade 3 gasoline. Available for production are 500 liters per hour grade 1 and 200 liters per hour of grade 2 and grade 3 each. Costs are 60 paise per liter for grade 1, 120 paise for grade 2 and100 paise for grade 3. Type A can be sold at Rs. 7.50 per liter and B can be sold at Rs. 9.00 per liter. How much of each fuel should be made and sold to maximise the profit. 2. A company manufactures two products X, and X, on three machines A, B, and C. X, require I hour on machine A and 1 hour on machine B and yields a revenue of Rs.3/-. Product X, requires 2 hours on machine A and 1 hour on machine B and 1 hour on machine Cand yields revenue of Rs. 5/-. In the coming planning period the available time of three machines A, B, and C are 2000 hours, 1500 hours and 600 hours respectively. Find the optimal product mix. 3. Maximize Z = 1 x+1 y S.T. 1x + 2 y < 2000 1x +1y s 1500 0 x +1 y s 600 and both x and y are > 0. 4. Maximise Z = 8000a + 7000b S.T. За+1bs 66 l a + 1 b < 45 1 a + 0b < 20 0 a + 1 b s 40 and both a and b are 2 0. 5. Minimise Z = 1.5 x + 2.5 y S.T. 1 x+ 3 y > 3 1x + 6 y 2 2 and both x and y > 0 6. Maximise Z= 3 a + 2 b S.T. la - 1 b s 1 l a + lb 2 3 and both x and y are 0 7. Maximise Z= -3 x + 2 y S.T. 1x +0 y s 3 1x -ly s 0 and both x and y are > 0 |||
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