MATHEMATICS · Subjective · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
A toy manufacturer produces two types of toys, A and B. Each toy of type A requires 2 labour-hours on machine I and 1 labour-hour on machine II. Each toy of type B requires 1 labour-hour on machine I and 2 labour-hours on machine II. In one production cycle, at most 10 labour-hours are available on machine I and at most 12 labour-hours are available on machine II. The profit on one toy of type A is ₹ 3 and on one toy of type B is ₹ 2.
(i) Formulate the above situation in terms of two variables x and y denoting the number of toys of types A and B respectively, and write all the constraints, including the non-negativity restrictions.
(ii) Draw the graph of the constraints obtained in part (i) and shade the feasible region.
(iii) List the coordinates of all vertices of the feasible region found in part (ii).
(iv) Calculate the profit at each vertex and hence determine the number of toys of each type that should be produced to obtain the maximum possible profit and the corresponding profit.