LINEAR PROGRAMMING
3.(15 points) Patrick Torres, a former QMIT Lecturer known as Boy Petiks, was bored one day. He talked about it with his closest summer friends, namely Manager, Boy Easy (Now known as Boy Medium), Boy Terror, Boy Intact, Boy Mentos, Boy Quant-Jay, Coach, Kerish, Vince, Gihoe, Girl, Salazar, Sean, and Stephen, and they all conducted some market research. One of the market opportunities they identified was the lack of solid bars in Katipunan, which are usually congested due to the high number of students in the area. After much advice and consultation, they decided to put up a new bar. After 69 failed attempts, they created and currently sell four kinds of mixed drinks, namely the Manager, the Easy, the Coach, and the Gin Bulag Petiks Special (GBPS), which each earn a profit of 120, 55, 50, and 15 pesos per drink sold, respectively. Table 1 lists the composition of each mixed drink as well as the available daily supply of each component. Easy Table 1: Drink component requirements and daily component supply Resource Usage per Drink Component Manager Coach GBPS Daily Supply Tequila 20 40 16,000 Rum 10 30 11,000 Vodka 40 30 10,000 Whisky 100 3,000 Gin 30 400 31,000 Coke 80 80 50 18,000 Sprite 40 50 12,000 Tonic 50 50 80 6,000 Because of the nature of their business and the dangers associated with excessive alcohol consumption, they also have to adhere to certain regulations: They can only produce up to 150 liters of mixed drinks per day. They can only produce up to 450 mixed drinks per day. The volume of Vodka used must not exceed the volume of Tequila used. The number of Gin Bulag Petiks Specials produced must not exceed 35% of the total number of mixed drinks produced. The total volume of Gin Bulag Petiks Specials produced must not exceed 65% of the total volume of mixed drinks produced. . If they need additional drink components, Bong, their supplier, is able to supply them with up to an additional 2 liters per drink component per day, up to a total of 10 liters per day, at the following prices: 120 pesos per liter of Tequila, Rum, or Vodka; 200 pesos per liter of Whisky; 20 pesos per liter of Gin; 30 pesos per liter of Coke or Sprite; 55 pesos per liter of Tonic. Lastly, in order to ensure that they, the owners of the bar, do not just drink all of the unused components themselves, Boy Petiks said that at least half of their stock of each component should be used. Formulate the scenario as a linear program. 3.(15 points) Patrick Torres, a former QMIT Lecturer known as Boy Petiks, was bored one day. He talked about it with his closest summer friends, namely Manager, Boy Easy (Now known as Boy Medium), Boy Terror, Boy Intact, Boy Mentos, Boy Quant-Jay, Coach, Kerish, Vince, Gihoe, Girl, Salazar, Sean, and Stephen, and they all conducted some market research. One of the market opportunities they identified was the lack of solid bars in Katipunan, which are usually congested due to the high number of students in the area. After much advice and consultation, they decided to put up a new bar. After 69 failed attempts, they created and currently sell four kinds of mixed drinks, namely the Manager, the Easy, the Coach, and the Gin Bulag Petiks Special (GBPS), which each earn a profit of 120, 55, 50, and 15 pesos per drink sold, respectively. Table 1 lists the composition of each mixed drink as well as the available daily supply of each component. Easy Table 1: Drink component requirements and daily component supply Resource Usage per Drink Component Manager Coach GBPS Daily Supply Tequila 20 40 16,000 Rum 10 30 11,000 Vodka 40 30 10,000 Whisky 100 3,000 Gin 30 400 31,000 Coke 80 80 50 18,000 Sprite 40 50 12,000 Tonic 50 50 80 6,000 Because of the nature of their business and the dangers associated with excessive alcohol consumption, they also have to adhere to certain regulations: They can only produce up to 150 liters of mixed drinks per day. They can only produce up to 450 mixed drinks per day. The volume of Vodka used must not exceed the volume of Tequila used. The number of Gin Bulag Petiks Specials produced must not exceed 35% of the total number of mixed drinks produced. The total volume of Gin Bulag Petiks Specials produced must not exceed 65% of the total volume of mixed drinks produced. . If they need additional drink components, Bong, their supplier, is able to supply them with up to an additional 2 liters per drink component per day, up to a total of 10 liters per day, at the following prices: 120 pesos per liter of Tequila, Rum, or Vodka; 200 pesos per liter of Whisky; 20 pesos per liter of Gin; 30 pesos per liter of Coke or Sprite; 55 pesos per liter of Tonic. Lastly, in order to ensure that they, the owners of the bar, do not just drink all of the unused components themselves, Boy Petiks said that at least half of their stock of each component should be used. Formulate the scenario as a linear program
