Q28 of 45 Page 1

A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has 30 and 17 units of workers (male and female) and capital respectively, which he uses to produce two types of goods A and B. To produce one unit of A, 2 workers and 3 units of capital are required while 3 workers and 1 unit of capital is required to produce one unit of B. If A and B are priced at ₹ 100 and ₹ 120 per unit respectively, how should he use his resources to maximise the total revenue? Form the above as an LPP and solve graphically. Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at the same rate?


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.


Constraints are:


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.


More from this chapter

All 45 →
26

Find the equation of the plane passing through the line of intersection of the planes and whose perpendicular distance from origin is unity.

OR


Find the vector equation of the line passing through the point (1, 2, 3) and parallel to the planes and

27

In a hockey match, both teams A and B scored same number of goals up to the end of the game, so to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the referee was fair or not.

 29

The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others and some others (say z) for supervising the workers to keep the colony neat and clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. If the sum of the number of awardees for honesty and supervision is twice the number of awardees for helping others, using matrix method, find the number of awardees of each category. Apart from these values, namely, honesty, cooperation and supervision, suggest one more value which the management of the colony must include for awards.

 9

If matrix and A2 = pA, then write the value of p.