Q. 294.7( 3 Votes )

A merchant plans

Answer :

Let x be the units be desktop demanded, and y be the units of


Portable model demanded.


According to a question we have the following objective function


and constraints.


Here the objective is to maximise profit.


Objective function: z = 4500x + 2500y


Constraint:


x + y ≤ 250


25000x + 40000y ≤ 70,00,000


5x + 8y ≤ 1400


x ≥ 0, y ≥ 0


The maximum value of z can only be obtained at the corner points of the feasible region. So we need to check the value of z at all corner points of the feasible region.


So, first, we will be finding out the feasible region by drawing the regions defined by constraints.


For plotting feasible region, we will be using the fundamentals of a straight line to get the feasible region as shown in the figure.




Clearly ABCD represents the feasible region and corner points are determined by solving:


x + y = 250 and 5x + 8y = 1400


x = 0 and 5x+8y = 1400


y = 0 and x + y = 250


& x = 0 and y = 0


To solve -


Value of objective function z


at point A = 4500(250) + 2500(0) = 1125000


Value of Z at point B = 4500×(200) + 2500(50) = 1150000


Value of Z at point C = 4500(0) + 2500(175) = 875000


Value of Z at point D = 4500×0 + 2500× 0 = 0


Z is maximum at point C (200,50)


Profit will be maximised for 200 units of x and 50 units of y and the maximum value of Z = maximum profit = Rs. 1150000


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