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Get Answers to all your Questions
4. A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:
| Types of toys | Machines | ||
| I | II | III | |
| A | 12 | 18 | 6 |
| B | 6 | 0 | 9 |
Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.
Answers (1)
Let x and y toys of type A and type B.
Mathematical formulation of given problem is as follows:
Minimize :
Subject to constraint ,
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
| corner points |
|
|
| |
150 | |
|
|
250 | |
| |
262.5 | maximum |
| |
200 |
Therefore 262.5 may or may not be maximum value of Z .
Hence , Z has maximum value 262.5 at point
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