A manufacturer can produce two products, A and B, during a given time period. Each of these products requires four different manufacturing operations: grinding, turning, assembling and testing. The manufacturing requirements in hours per unit of products A and B are given below.

A | B | |

Grinding | 1 | 2 |

Turning | 3 | 1 |

Assembling | 6 | 3 |

Testing | 5 | 4 |

The available capacities of these operations in hours for the given time period are: grinding 30; turning 60, assembling 200; testing 200. The contribution to profit is Rs 20 for each unit of A and Rs 30 for each unit of B. The firm can sell all that it produces at the prevailing market price. Determine the optimum amount of A and B to produce during the given time period. Formulate this as a LPP.

Asked by Sakshi | 1 year ago | 79

Let x and y units of products A and B were manufactured respectively.

The contribution to profit is Rs 2 for each unit of A and Rs 3 for each unit of B.

Therefore for x units of A and y units of B,the contribution to profit would be Rs 2x and Rs 3y respectively.

Let Z denote the total profit

Then, Z = Rs (2x + 3y)

Total hours required for grinding, turning, assembling and testing are x+2y, 3x+y, 6x+3y, 5x+4yx+2y, 3x+y, 6x+3y, 5x+4y respectively.

The available capacities of these operations in hours for the given period are grinding 30, turning 60, assembling 200 and testing 200.

x+2y≤30,

3x+y≤60, 6x+3y≤200,

5x+4y≤200x+2y≤30,

3x+y≤60, 6x+3y≤200,

5x+4y≤200

Units of products cannot be negative.Therefore,

x,y≥0x,y≥0

Hence, the required LPP is as follows:

Maximize Z = 2x + 3y

subject to

x+2y≤30,

3x+y≤60,

6x+3y≤200,

5x+4y≤200

Answered by Aaryan | 1 year agoMinimize Z = 2x + 4y

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