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प्रश्न
A manufacturing company makes two types of television sets; one is black and white and the other is colour. The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a coloured set. The company can spend not more than Rs 648000 a week to make television sets. If it makes a profit of Rs 510 per black and white set and Rs 675 per coloured set, how many sets of each type should be produced so that the company has maximum profit? Formulate this problem as a LPP given that the objective is to maximise the profit.
उत्तर
The problem is: Maximise Z = 510x + 675y
Subject to the constraints: `{:(x + y ≤ 300),(2x + 3y ≤ 720),(x ≥ 0"," y ≥ 0):}}`
The feasible region OABC is shown in the Figure
Since the feasible region is bounded
Therefore maximum of Z must occur at the corner point of OBC.
| Corner Point | Value of Z | |
| O(0, 0) | 510 (0) + 675 (0) = 0 | |
| A(300, 0) | 510 (300) + 675 (0) = 153000 | |
| B(180, 120) | 510 (180) + 675 (120) = 172800 | ← Maximum |
| C(0, 240) | 510 (0) + 675 (240) = 162000 |
Thus, maximum Z is 172800 at the point (180, 120), i.e., the company should produce 180 black and white television sets and 120 coloured television sets to get maximum profit.
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