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QUESTION 2 (66 MARKS) 2.1 Formulate the following problem as a linear programming problem. Do not solve it! Sky Aviation Industries has two plants, I and II, which produce the "Venag" jet engines used in their light commercial airplanes. The maximum capacities of these two plants are 100 units and 110 units per month, respectively. The engines are shipped to two of the company's main assembly plants, A and B. The shipping costs (in dollars) per engine from plants I and II to the main assembly plants A and B are as follows: To A B From I [100 60] II [120 70] In a certain month, assembly plant A needs 80 engines while assembly plant B needs 70 engines. Set up a linear programming model that will determine the number of engines to be shipped from each plant to each main assembly plant that will minimise the total cost. (15 marks) 2.2 Cassy Finance Company has a total of N$20 million earmarked for home loans and automobile loans. On the average, home loans will have a 10% rate of return on the loans given out while automobile loans will yield a 12% rate of return on the loans extended. Management has also stipulated that the total amount of home loans should be atleast four times the total amount of automobile loans. Use the graphical method to determine the total amount of loans the company should extend to each of the two categories of customers in order to maximise the rate of return on the loans extended. (15 marks) 2.3 A fruit juice company makes two special drinks by blending apple and pineapple juices. The first drink uses 30% apple juice and 70% pineapple juice, while the second drink uses 60% apple juice and 40% pineapple juice. There are 1000 liters of apple juice and 1500 liters of pineapple juice available. If the profit for the first drink is N$.60 per liter and that for the second drink is N$.50, use the simplex method to find the number of liters of each drink that should be produced in order to maximize the profit. (15 marks) 2.4 Determine the dual problem of the linear programming problem below: Minimise C = 4x + 2y + 6z Subject to x + 2y + z ? 4 2x + y + 2z ? 2 3x + 2y + z ? 3 x, y, z ? 0 (6 marks) 2.5 Use the dual method to solve the problem in question 2.4. (15 marks)

          QUESTION 2 (66 MARKS)

2.1 Formulate the following problem as a linear programming problem. Do not solve it!
Sky Aviation Industries has two plants, I and II, which produce the "Venag" jet engines used in their light commercial airplanes. The maximum capacities of these two plants are 100 units and 110 units per month, respectively. The engines are shipped to two of the company's main assembly plants, A and B. The shipping costs (in dollars) per engine from plants I and II to the main assembly plants A and B are as follows:

To
A B
From I [100 60]
II [120 70]

In a certain month, assembly plant A needs 80 engines while assembly plant B needs 70 engines. Set up a linear programming model that will determine the number of engines to be shipped from each plant to each main assembly plant that will minimise the total cost.
(15 marks)

2.2 Cassy Finance Company has a total of N$20 million earmarked for home loans and automobile loans. On the average, home loans will have a 10% rate of return on the loans given out while automobile loans will yield a 12% rate of return on the loans extended. Management has also stipulated that the total amount of home loans should be atleast four times the total amount of automobile loans. Use the graphical method to determine the total amount of loans the company should extend to each of the two categories of customers in order to maximise the rate of return on the loans extended.
(15 marks)

2.3 A fruit juice company makes two special drinks by blending apple and pineapple juices. The first drink uses 30% apple juice and 70% pineapple juice, while the second drink uses 60% apple juice and 40% pineapple juice. There are 1000 liters of apple juice and 1500 liters of pineapple juice available. If the profit for the first drink is N$.60 per liter and that for the second drink is N$.50, use the simplex method to find the number of liters of each drink that should be produced in order to maximize the profit.
(15 marks)

2.4 Determine the dual problem of the linear programming problem below:
Minimise C = 4x + 2y + 6z
Subject to x + 2y + z ? 4
2x + y + 2z ? 2
3x + 2y + z ? 3
x, y, z ? 0
(6 marks)

2.5 Use the dual method to solve the problem in question 2.4.
(15 marks)

QUESTION 2 (66 MARKS)

2.1 Formulate the following problem as a linear programming problem. Do not solve it!
Sky Aviation Industries has two plants, I and II, which produce the "Venag" jet engines used in their light commercial airplanes. The maximum capacities of these two plants are 100 units and 110 units per month, respectively. The engines are shipped to two of the company's main assembly plants, A and B. The shipping costs (in dollars) per engine from plants I and II to the main assembly plants A and B are as follows:

To
A B
From I [100 60]
II [120 70]

In a certain month, assembly plant A needs 80 engines while assembly plant B needs 70 engines. Set up a linear programming model that will determine the number of engines to be shipped from each plant to each main assembly plant that will minimise the total cost.
(15 marks)

2.2 Cassy Finance Company has a total of N20 million earmarked for home loans and automobile loans. On the average, home loans will have a 10% rate of return on the loans given out while automobile loans will yield a 12% rate of return on the loans extended. Management has also stipulated that the total amount of home loans should be atleast four times the total amount of automobile loans. Use the graphical method to determine the total amount of loans the company should extend to each of the two categories of customers in order to maximise the rate of return on the loans extended.
(15 marks)

2.3 A fruit juice company makes two special drinks by blending apple and pineapple juices. The first drink uses 30% apple juice and 70% pineapple juice, while the second drink uses 60% apple juice and 40% pineapple juice. There are 1000 liters of apple juice and 1500 liters of pineapple juice available. If the profit for the first drink is N$.60 per liter and that for the second drink is N$.50, use the simplex method to find the number of liters of each drink that should be produced in order to maximize the profit.
(15 marks)

2.4 Determine the dual problem of the linear programming problem below:
Minimise C = 4x + 2y + 6z
Subject to x + 2y + z ? 4
2x + y + 2z ? 2
3x + 2y + z ? 3
x, y, z ? 0
(6 marks)

2.5 Use the dual method to solve the problem in question 2.4.
(15 marks)

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