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The BBK Hot Sauce Company can produce three types of hot sauce, the Heatwave, the Inferno and the Megahot. Each batch is made using jalepeño peppers and scotch bonnet peppers. The number of boxes of jalepeño peppers and scotch bonnet peppers required to produce one batch of each type is given in the following table. Sauce Type Jalepeño Peppers Scotch Bonnet Peppers Heatwave 14 Inferno 7 Megahot 17 9 18 11 Every week there are 2000 boxes of jale peño peppers and 1400 boxes of scotch bon- net peppers available. Each box of jalepeño peppers costs £5 and each box of scotch bonnet peppers costs £7. Each batch has to go through three processes during production: chopping, boiling and blending. The number of hours required in each process to produce one batch of each type is given in the following table. Sauce Type Heatwave Inferno Megahot Chopping Chopping | Boiling | Blending 2 3 2 Tr 1 1 1 2 3 3 Every week the number of hours of labour available for each process are: 75 for chop- ping, 90 for boiling and 45 for blending. For each process, an hour of labour costs £11. Each batch of Heatwave sells for £275, each batch of Inferno sells for £260 and each batch of Megahot sells for £350, and the company can sell all of the batches it pro- duces. Given that the BBK Hot Sauce Company wants to maximize the weekly profit from hot sauce production, and the only costs are for labour and boxes of jalepeño peppers and scotch bonnet peppers, find a linear programme that can be used to determine the weekly production strategy for batches of hot sauce, explaining clearly what each vari- able and each constraint represents. (You do not have to solve the linear programme.)

The BBK Hot Sauce Company can produce three types of hot sauce, the Heatwave, the Inferno and the Megahot. Each batch is made using jalepeño peppers and scotch bonnet peppers. The number of boxes of jalepeño peppers and scotch bonnet peppers required to produce one batch of each type is given in the following table. Sauce Type Jalepeño Peppers Scotch Bonnet Peppers Heatwave 14 Inferno 7 Megahot 17 9 18 11 Every week there are 2000 boxes of jale peño peppers and 1400 boxes of scotch bon- net peppers available. Each box of jalepeño peppers costs £5 and each box of scotch bonnet peppers costs £7. Each batch has to go through three processes during production: chopping, boiling and blending. The number of hours required in each process to produce one batch of each type is given in the following table. Sauce Type Heatwave Inferno Megahot Chopping Chopping | Boiling | Blending 2 3 2 Tr 1 1 1 2 3 3 Every week the number of hours of labour available for each process are: 75 for chop- ping, 90 for boiling and 45 for blending. For each process, an hour of labour costs £11. Each batch of Heatwave sells for £275, each batch of Inferno sells for £260 and each batch of Megahot sells for £350, and the company can sell all of the batches it pro- duces. Given that the BBK Hot Sauce Company wants to maximize the weekly profit from hot sauce production, and the only costs are for labour and boxes of jalepeño peppers and scotch bonnet peppers, find a linear programme that can be used to determine the weekly production strategy for batches of hot sauce, explaining clearly what each vari- able and each constraint represents. (You do not have to solve the linear programme.)

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 51P
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The BBK Hot Sauce Company can produce three types of hot sauce, the Heatwave, the Inferno and the Megahot. Each batch is made using jalepeño peppers and scotch bonnet peppers. The number of boxes of jalepeño peppers and scotch bonnet peppers required to produce one batch of each type is given in the following table. Sauce Type Jalepeño Peppers Scotch Bonnet Peppers Heatwave 14 Inferno Megahot 9 18 11 Every week there are 2000 boxes of jalepeño peppers and 1400 boxes of scotch bon- net peppers available. Each box of jalepeño peppers costs £5 and each box of scotch bonnet peppers costs £7. 7 17 Each batch has to go through three processes during production: chopping, boiling and blending. The number of hours required in each process to produce one batch of each type is given in the following table. Inferno Megahot Sauce Type Chopping | Boiling | Blending Heatwave 2 3 1 ?? 1 3 2 3 Every week the number of hours of labour available for each process are: 75 for chop- ping, 90 for boiling and 45 for blending. For each process, an hour of labour costs £11. Each batch of Heatwave sells for £275, each batch of Inferno sells for £260 and each batch of Megahot sells for £350, and the company can sell all of the batches it pro- duces. Given that the BBK Hot Sauce Company wants to maximize the weekly profit from hot sauce production, and the only costs are for labour and boxes of jalepeño peppers and scotch bonnet peppers, find a linear programme that can be used to determine the weekly production strategy for batches able and each constraint represents. (You hot sauce, explaining clearly what each vari- do not have to solve the linear programme.)
Transcribed Image Text:The BBK Hot Sauce Company can produce three types of hot sauce, the Heatwave, the Inferno and the Megahot. Each batch is made using jalepeño peppers and scotch bonnet peppers. The number of boxes of jalepeño peppers and scotch bonnet peppers required to produce one batch of each type is given in the following table. Sauce Type Jalepeño Peppers Scotch Bonnet Peppers Heatwave 14 Inferno Megahot 9 18 11 Every week there are 2000 boxes of jalepeño peppers and 1400 boxes of scotch bon- net peppers available. Each box of jalepeño peppers costs £5 and each box of scotch bonnet peppers costs £7. 7 17 Each batch has to go through three processes during production: chopping, boiling and blending. The number of hours required in each process to produce one batch of each type is given in the following table. Inferno Megahot Sauce Type Chopping | Boiling | Blending Heatwave 2 3 1 ?? 1 3 2 3 Every week the number of hours of labour available for each process are: 75 for chop- ping, 90 for boiling and 45 for blending. For each process, an hour of labour costs £11. Each batch of Heatwave sells for £275, each batch of Inferno sells for £260 and each batch of Megahot sells for £350, and the company can sell all of the batches it pro- duces. Given that the BBK Hot Sauce Company wants to maximize the weekly profit from hot sauce production, and the only costs are for labour and boxes of jalepeño peppers and scotch bonnet peppers, find a linear programme that can be used to determine the weekly production strategy for batches able and each constraint represents. (You hot sauce, explaining clearly what each vari- do not have to solve the linear programme.)
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