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Question

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 350 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 500 per black and white set and Rs 600 per coloured set. Formulate this problem as an LPP given that the objective is to maximise the profit. what is the maximum profit ?

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Solution

The correct option is **A** 177000

Let x and y denote, respectively, the number of black and white sets and

coloured sets made each week. Thus

x ≥ 0, y ≥ 0

Since the company can make at most 350 sets a week, therefore,

x + y ≤ 350

Weekly cost (in Rs) of manufacturing the set is

1800x + 2700y

and the company can spend up to Rs. 648000. Therefore,

1800x + 2700y ≤ 648000, i.e., or 2x + 3y ≤ 720

The total profit on x black and white sets and y colour sets is Rs (500x + 600y). Let

Z = 500x + 600y . This is the objective function.

Thus, maximum Z is 177000 at the point (330, 20), hence company should produce 330 black and white television sets and 20 coloured television sets to get maximum profit.

Let x and y denote, respectively, the number of black and white sets and

coloured sets made each week. Thus

x ≥ 0, y ≥ 0

Since the company can make at most 350 sets a week, therefore,

x + y ≤ 350

Weekly cost (in Rs) of manufacturing the set is

1800x + 2700y

and the company can spend up to Rs. 648000. Therefore,

1800x + 2700y ≤ 648000, i.e., or 2x + 3y ≤ 720

The total profit on x black and white sets and y colour sets is Rs (500x + 600y). Let

Z = 500x + 600y . This is the objective function.

Corner Point | Z = 500x+600y |

(0, 240) | 144000 |

(330, 20) | 177000 |

(350, 0) | 175000 |

Thus, maximum Z is 177000 at the point (330, 20), hence company should produce 330 black and white television sets and 20 coloured television sets to get maximum profit.

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