Mrs Rb
1 DEFINITION OF LINEAR PROGRAMMING (LP)
Linear programming (LP) is a mathematical technique used in finding the best possible allocation of resources to achieve the best outcome, which is maximising profit or minimising cost. However, it is only applicable where there is a linear relationship between the variables. For example, the linear relationships between hours of labour and output in a textiles factory means an increase or decrease in labour force has a direct impact on production, which is the output. Due to the constraints, it is essential to solve the linear programming problem and find the feasible region of the objective function.
2 ANSWER (A) OPTIMAL PROFIT
Calculations
Brass Ltd produces two products, the Masso product and the Russo product. Masso ($) Russo ($)
Selling Prices 150 100
Materials 80 30
Salesmen's Commission 30 20
Profit 40 50
Let ‘M’ represent the Masso products ‘R’ represent the Russo products ‘Z’ represent the objective function
Profit, Z = 40M + 50R
Constraint: Machining M + 2R ≤ 700 Assembly 2.5M + 2R ≤ 1000 Non- negativity M ≥ 0 R ≥ 0
Machine constraints
Use equation 1 if Brass Ltd will produce M = 0 product M + 2R = 700 0 + 2R = 700 R = 700/2 R = 350
(Brass Ltd can produce 350 units of Russo products if not producing Masso products)
Use equation 1 if Brass Ltd will produce R = 0 products M + 2R = 700 M + 2(0) = 700 M = 700
(700 units of Masso products can be produced if Brass Ltd is not producing Russo products)
Therefore, (M, R) = (700, 350)
Assembly Constraint
Use equation 2 if Brass Ltd will produce M = 0 product 2.5M + 2R = 1000 2.5(0) + 2R = 1000 2R = 1000 R = 500
(Brass Ltd can assemble 500 units of Russo products in 2 hours if not producing Masso products)
Use equation 2 if Brass Ltd will produce R = 0 products 2.5M + 2R = 1000 2.5M + 2(0)
Linear programming (LP) is a mathematical technique used in finding the best possible allocation of resources to achieve the best outcome, which is maximising profit or minimising cost. However, it is only applicable where there is a linear relationship between the variables. For example, the linear relationships between hours of labour and output in a textiles factory means an increase or decrease in labour force has a direct impact on production, which is the output. Due to the constraints, it is essential to solve the linear programming problem and find the feasible region of the objective function.
2 ANSWER (A) OPTIMAL PROFIT
Calculations
Brass Ltd produces two products, the Masso product and the Russo product. Masso ($) Russo ($)
Selling Prices 150 100
Materials 80 30
Salesmen's Commission 30 20
Profit 40 50
Let ‘M’ represent the Masso products ‘R’ represent the Russo products ‘Z’ represent the objective function
Profit, Z = 40M + 50R
Constraint: Machining M + 2R ≤ 700 Assembly 2.5M + 2R ≤ 1000 Non- negativity M ≥ 0 R ≥ 0
Machine constraints
Use equation 1 if Brass Ltd will produce M = 0 product M + 2R = 700 0 + 2R = 700 R = 700/2 R = 350
(Brass Ltd can produce 350 units of Russo products if not producing Masso products)
Use equation 1 if Brass Ltd will produce R = 0 products M + 2R = 700 M + 2(0) = 700 M = 700
(700 units of Masso products can be produced if Brass Ltd is not producing Russo products)
Therefore, (M, R) = (700, 350)
Assembly Constraint
Use equation 2 if Brass Ltd will produce M = 0 product 2.5M + 2R = 1000 2.5(0) + 2R = 1000 2R = 1000 R = 500
(Brass Ltd can assemble 500 units of Russo products in 2 hours if not producing Masso products)
Use equation 2 if Brass Ltd will produce R = 0 products 2.5M + 2R = 1000 2.5M + 2(0)