The cement additive, Tuf should not contain more than 70% of Lime and the cement additive, Rok must contain at least 45% of Flyash. The company can sell at most 8000kg of its additive products (Tuf and Rok) per hour. There are other limitations and local requirements, as stated below: a) Due to the plant installed capacity and personnel requirements, no more than 6000 kg/hour of Tuf can be produced b) The plant has contracted to deliver at least 3500 kg/hour of Tuf c) The company is restricted, by local ordinance, from producing more than 2000 kg of additive Rok per hour. Formulate an LP model to prescribe a production plan that minimizes the cost of operations (the total cost of purchasing Oikcem and Plascem).
The cement additive, Tuf should not contain more than 70% of Lime and the cement additive, Rok must contain at least 45% of Flyash. The company can sell at most 8000kg of its additive products (Tuf and Rok) per hour. There are other limitations and local requirements, as stated below: a) Due to the plant installed capacity and personnel requirements, no more than 6000 kg/hour of Tuf can be produced b) The plant has contracted to deliver at least 3500 kg/hour of Tuf c) The company is restricted, by local ordinance, from producing more than 2000 kg of additive Rok per hour. Formulate an LP model to prescribe a production plan that minimizes the cost of operations (the total cost of purchasing Oikcem and Plascem).
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![A cement mix company is renowned for providing high strength concrete additives - at high unit cost. It delivers two types of
cement additives - Tuf and Rok. In making these additives the company adds two special products, Qikcem and Plascem.
These additives contain two (2) basic ingredients: Lime and Flyash, in different proportions, as shown in the table below.
Flyash
[%]
Lime
Cost
Special Products
Qikcem (1)
Plascem (2)
Availability
[kg/hr]
2600
3600
[%]
[S/kg]
10
15
45
55
35
65
The cement additive, Tuf should not contain more than 70% of Lime and the cement additive, Rok must contain at
least 45% of Flyash. The company can sell at most 800oerkg of its additive products (Tuf and Rok) per hour. There are
other limitations and local requirements, as stated beklew:
a) Due to the plant installed capacity and personnel requirements, no more than 6000 kg/hour of Tuf can be
produced
b) The plant has contracted to deliver at least 3500 kg/hour of Tuf
c)
The company is restricted, by local ordinance, from producing more than 2000 kg of additive Rok per hour.
Formulate an LP model to prescribe a production plan that minimizes the cost of operations (the total cost of
purchasing Qikcem and Plascem).
Define the variables as follows (You may add other variables but you must use these).
LET:
X1T = Amount (kg) of Qikcem used to produce Tuf
X2T
Amount (kg) of Plascem used to produce Tuf
X1R = Amount (kg).of Qikcem used to produce Rok
X2R = Amount (kg) of Plascem used to produce Rok](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F388a9fab-648d-450d-a1a5-3932044f3fea%2Fac411cf8-4654-429a-a961-76086d717b07%2F553lzbe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A cement mix company is renowned for providing high strength concrete additives - at high unit cost. It delivers two types of
cement additives - Tuf and Rok. In making these additives the company adds two special products, Qikcem and Plascem.
These additives contain two (2) basic ingredients: Lime and Flyash, in different proportions, as shown in the table below.
Flyash
[%]
Lime
Cost
Special Products
Qikcem (1)
Plascem (2)
Availability
[kg/hr]
2600
3600
[%]
[S/kg]
10
15
45
55
35
65
The cement additive, Tuf should not contain more than 70% of Lime and the cement additive, Rok must contain at
least 45% of Flyash. The company can sell at most 800oerkg of its additive products (Tuf and Rok) per hour. There are
other limitations and local requirements, as stated beklew:
a) Due to the plant installed capacity and personnel requirements, no more than 6000 kg/hour of Tuf can be
produced
b) The plant has contracted to deliver at least 3500 kg/hour of Tuf
c)
The company is restricted, by local ordinance, from producing more than 2000 kg of additive Rok per hour.
Formulate an LP model to prescribe a production plan that minimizes the cost of operations (the total cost of
purchasing Qikcem and Plascem).
Define the variables as follows (You may add other variables but you must use these).
LET:
X1T = Amount (kg) of Qikcem used to produce Tuf
X2T
Amount (kg) of Plascem used to produce Tuf
X1R = Amount (kg).of Qikcem used to produce Rok
X2R = Amount (kg) of Plascem used to produce Rok
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