According to the question we can frame the following objective function and the constraints as given below.
Objective function is: z = 100x + 120y
Where x represents number of units of capital A and y represents number of units of capital B
While taking sense of worker x represents number of male and y is for females.
2x + 3y ≤ 30
3x + y ≤ 17
x ≥ 0, y ≥ 0
maximum value of z can only be obtained at the corner points of feasible region. So we need to check value of z at all corner points of 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 straight line to get the feasible region as shown in figure.
Clearly ABCD represents the feasible region and corner points are determined by solving:
3x+y = 17 and 2x + 3y = 30
x = 0 and 2x+3y = 30
y = 0 and 3x+y = 17
& x = 0 and y = 0
To solve -
∴Value of objective function z at point A =
Value of Z at point B = 100×(3) + 120(8) = 1260
Value of Z at point C = 100× 0 + 120× 10 = 1200
Value of Z at point D = 100×0 + 120× 0 = 0
Clearly Z is maximum at point C (3,8)
∴ revenue will be maximised for 3 units of x and 8 units of y
And maximum value of Z = maximum revenue = Rs. 1260
Yes, I completely agree with the view that both male and female must be paid equally and there should not be any discrimination based on gender.
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