An organisation produces X1 and X2 units of products R and S, respectively. In this case, the objective function and constraints are expressed as follows:
- An organisation produces X1 and X2 units of products R and S, respectively. In this case, the objective function and constraints are expressed as follows:
Maximise
Maximise Z = 60X1 + 120X2
Subject to, 3X1 + 6X2 ≤ 240 Raw material constraint
2X1 + 4X2 ≤ 800 Labour hours constraint
X1, X2 ≥ 0 Non-negativity condition
Use graphical method to determine how many units of products R and S the organisation should produce to maximise its profits.
Answer 2(b) – Here,
Let us plot the constraint lines on a graph by calculating the values of x1 and x2 with the help of the terminal points. The calculation of x1 and x2 values with the help of terminal points is given as follows:
For constraint equation: 3X1 + 6X2 ≤ 240 ,
Substitute x1 = 0 in the equation, then x2 = 240/6
X2 = 40
In case, substituting x2 = 0,
Then, x1 = 240/3
X1 = 80
Similarly, for constraint equation 2×1 + 4×2 ≤800,
substituting x1 = 0, Then, x2 = 800/4
x2 = 200
In case, substituting x2 = 0,
Then, x1 = 800/2
x1 = 400
Let us plot the calculated equations of x1 and x2 on a graph, which is shown in Fig——————
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