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Linear Programming (LP)

Question 1

Solve the following LP problem graphically.

Minimise Z = 5x + 3y

Subject to the following constraints:

x + y ≤ 20
x ≥ 2
y ≥ 4x
x, y ≥ 0

What are the exact coordinates of the vertices of feasible region (3 marks)

What is the value of Z (2 marks)

A car manufacturing company makes two models X and Y. Model X requires 8 labour hours for fabricating/assembling and 1 labour hour for finishing/testing. Model Y requires 12 labour hours for fabricating/assembling and 3 labour hours for finishing/testing. For fabricating/assembling the maximum labour hours available is 220. For finishing/testing, the maximum labour hours available is 35. The company warehouse has a maximum capacity per week of holding 20 manufactured cars of model X and Y, and makes a profit of £18,500 on selling each model X and £21,400 on selling each Model Y.

Formulate this problem as a Linear Programming problem by stating and writing out the Objective Function and all the Constraints. (5 marks)

How many Model X and Model Y should be manufactured per week to realise a maximum profit. (3 marks)

What is the maximum profit. (2 marks)

Question 2

An aircraft can carry maximum of 250 passengers. A profit of £3,500 is made on each executive class; £1,000 for each business class; and £600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class and another 30 for business class. However, at least 5 times as many passengers prefer to travel by economy class than by the executive class. Space capacity means that the total seats for executive and business cannot exceed 100.

Executives are allowed 50kg of luggage; business is 35kg; and economy 23kg, for safety reason the total luggage for all the passengers cannot exceed 7,500kg. You are to determine how many tickets of each class that must be sold in order to maximise the profit for the airline, and the maximum profit?

Formulate this problem as a Linear Programming problem by stating the objective function and write out all the constraints. (7 marks)

Using Excel Solver determine
Determine how many tickets of each class that must be sold in order to maximise the profit for the airline. (5 marks)

What is the maximum profit. (3 marks)

2020 Exams Questions (Resit)

Question 3

Solve the following LP problem graphically.

Maximise Z = 5x + 3y

Subject to the following constraints:

x + y ≤ 36
x ≥ 2
y ≥ 5x
x, y ≥ 0

What are the exact coordinates of the vertices of feasible region (3 marks)

What is the value of Z (2 marks)

A car manufacturing company makes two models X and Y. Model X requires 8 labour hours for fabricating/assembling and 1 labour hour for finishing/testing. Model Y requires 10 labour hours for fabricating/assembling and 2 labour hours for finishing/testing.

For fabricating/assembling the maximum labours available is 250. For finishing/testing, the maximum labour hours available is 40. The company warehouse has a maximum capacity per week of holding 30 manufactured cars of model X and Y, and makes a profit of £19,500 on selling each model X and £23,500 on selling each Model Y.

Formulate this problem as a Linear Programming problem by stating and writing out the Objective Function and all the constraints. (5 marks)

How many Model X and Model Y should be manufactured per week to realise a maximum profit. (3 marks)

What is the maximum profit. (2 marks)

Question 4

An aircraft can carry maximum of 200 passengers. A profit of £3,000 is made on each executive class; £1,000 for business class; and £800 is made on each economy class ticket. The airline reserves at least 20 seats for executive class and another 30 for business. However, at least 3 times as many passengers prefer to travel by economy class than by the executive class. Space capacity means that the total seats for executive and business cannot exceed 80.

Executives are allowed 50kg of luggage; business is 35kg; and economy 23kg, for safety reason the total luggage for all the passengers cannot exceed 7,000kg. Determine how many tickets of each type must be sold in order to maximise the profit for the airline.

Formulate this problem as a Linear Programming problem by stating the objective function and write out all the constraints. (7 marks)

Using Excel Solver determine

Determine how many tickets of each type that must be sold in order to maximise the profit for the airline. (5 marks)

What is the maximum profit. (3 marks)