Question

a company producing two products A and B to manufacture a product certain machine has to be utilized for 1.5 hours and a labor time of 2 hours to manufacture a product B the machine has to be utilized for 2.5 hours and labor time of 1.5 hours

Answer 1

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Regardless of the way one defines linear programming, certain basic requirements which are given below are necessary before the technique can be employed for optimization problems.

(1) Decision Variable and their Relationship:

(2) Well-Defined Objective Function:

(3) Presence of Constraints or Restrictions:

Answer 2

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Let

•x be the number of units of X produced in the current week

•y be the number of units of Y produced in the current week

then the constraints are:

•50x + 24y <= 40(60) machine A time

•30x + 33y <= 35(60) machine B time

•x >= 75 - 30

•i.e. x >= 45 so production of X >= demand (75) - initial stock (30), which ensures we meet demand

•y >= 95 - 90

•i.e. y >= 5 so production of Y >= demand (95) - initial stock (90), which ensures we meet demand

• The objective is:

maximise (x+30-75) + (y+90-95) = (x+y-50)

i.e. to maximise the number of units left in stock at the end of the week

It is plain from the diagram below that the maximum occurs at the intersection of x=45 and 50x + 24y = 2400

Solving simultaneously, rather than by reading values off the graph, we have that x=45 and y=6.25 with the value of the objective function being 1.25

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