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Question :
A company uses the linear programming model to find the optimal production plan for its two products X and Y. The model considers ‘x’ to be number of units of product X and ‘y’ to be the number of units of product Y.
It has identified the following equations:
Objective function = Maximise 8x + 12y
Subject to the following constraints:
Material 2x + y ? 2,000
Unskilled labour: x + y ? 1,500
and x ? 400
What is the optimal solution for the output of X and Y?
My answer was :
I worked out all the constraints and resulted in x = 400 , y = 1200 since it give the highest contribution when working the objective function.Material 2x + y = 2000
when y = 0 when x = 400
x =1000.00 y = 1200.00
Objective functions
8,000.00 17,600.00Labour
when y = 0 when x = 400
x = 1,500.00 y= 1,100.00
Objective functions
12,000.00 16,400.00Material 2x + y = 2000 2x + y = 2000
Labour x + y = 1500 x2 2x + 2y = 3000y = 1000
2x = 1000
x = 500Objective function 16.000,00
Correct answer is x=400, y = 1100
Material 2x + y < 2,000 – (material is lower or equal to)
Unskilled labour: x + y < 1,500 (labour is lower or equal to)
and x > 400 (greater or equal to)
Your answer (x = 400, y = 1,200) cannot be correct because then x + y is more than 1,500.
You are assuming that the optimum solution is where the material line crosses the labour line, but this does not have to be the case – it is at one of the corners of the feasibly region, but it could be at any of the corners (depending on the angle of the objective line).
Have you watched my free lectures on linear programming, because I do explain this point?
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