jellytelly
New member
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- Nov 21, 2011
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I'm stuck wit section b and c.
The SIM Company (SC) makes two types of tonic drinks, namely G-force and Black Bull. The same raw material inputs, rehmannia glutinosa and cordyceps sinensis, and the same production line, are used in the manufacture of both drinks. Each production day, one ton of rehmannia glutinosa and two tons of cordyceps sinensis are available. Each litre of G-force requires 8 kg of rehmannia glutinosa and 32 kg of cordyceps sinensis, while a litre of Black Bull uses 12 kg of rehmannia glutinosa and 19 kg of cordyceps sinensis (assume 1 ton = 1000 kg).
SC’s production day is 8 full hours. Its production line can turn out 25 litres of G-force or 20 litres of Black Bull, per hour. Only one product can be made at a time, but the line is easily changed from one item to the other. Forecasts indicate that demand for G-force and Black Bull far exceeds production capacity. The profit per litre of G-force is $30 and per litre of Black Bull is $36.
Management Scientist’s Printout:
Objective coefficient ranges
The first part is on the liner programming model to max profit.
the answer I worked out .
X1 = production of g-force
X2 = production of black bull
Max z = 30X1 + 36X2
s.t 8X1 + 12X2 < 1000 (max rehmannia gultinosa)
32X1 + 19X2 < 2000 (max cordyceps sinensis)
0.04X1 + 0.05X2 < 8 (max production line)
X1,X2 > 0 (non-negativity)
(b) Given the optimal solution lies at the intersection of raw material inputs, rehmannia glutinosa and cordyceps sinensis, determine the optimal production level for G-Force and Black Bull.
(c) What is the optimal profit for SIM Company?
For the two parts I need help, don't quite understand.
Thanks.
The SIM Company (SC) makes two types of tonic drinks, namely G-force and Black Bull. The same raw material inputs, rehmannia glutinosa and cordyceps sinensis, and the same production line, are used in the manufacture of both drinks. Each production day, one ton of rehmannia glutinosa and two tons of cordyceps sinensis are available. Each litre of G-force requires 8 kg of rehmannia glutinosa and 32 kg of cordyceps sinensis, while a litre of Black Bull uses 12 kg of rehmannia glutinosa and 19 kg of cordyceps sinensis (assume 1 ton = 1000 kg).
SC’s production day is 8 full hours. Its production line can turn out 25 litres of G-force or 20 litres of Black Bull, per hour. Only one product can be made at a time, but the line is easily changed from one item to the other. Forecasts indicate that demand for G-force and Black Bull far exceeds production capacity. The profit per litre of G-force is $30 and per litre of Black Bull is $36.
Management Scientist’s Printout:
Objective coefficient ranges
| Variable | Lower limit | Current limit | Upper Limit |
| X1 | 24.000 | 30.000 | 60.632 |
| X2 | 17.813 | 36.000 | 45.000 |
The first part is on the liner programming model to max profit.
the answer I worked out .
X1 = production of g-force
X2 = production of black bull
Max z = 30X1 + 36X2
s.t 8X1 + 12X2 < 1000 (max rehmannia gultinosa)
32X1 + 19X2 < 2000 (max cordyceps sinensis)
0.04X1 + 0.05X2 < 8 (max production line)
X1,X2 > 0 (non-negativity)
(b) Given the optimal solution lies at the intersection of raw material inputs, rehmannia glutinosa and cordyceps sinensis, determine the optimal production level for G-Force and Black Bull.
(c) What is the optimal profit for SIM Company?
For the two parts I need help, don't quite understand.
Thanks.
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