# A manufacturer ma

let x and y be the number of toys manufactured per day of type A and B respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:

Maximize Z = 7.5x + 5y ….(1)

Subject to the constraints,

2x + y ≤ 60 …..(2)

x ≤ 60 …..(3)

2x + 3y ≤ 120 ….(4)

x ≥ 0, y ≥ 0 ….(5)

Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.

The coordinates of the corner points A(20,0),B(20,20), C(15,30)and D(0,40).

Now, we find the maximum value of Z. According to table the maximum value of Z = 262.5 at point C (15,30).

Hence, 15 and 20 be the number of toys manufactured per day of type A and B respectively to get the maximum profit.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

A manufacturer prMathematics - Board Papers

A retired person Mathematics - Board Papers

A manufacturing cMathematics - Board Papers