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.
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.
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.
Units of products cannot be negative.Therefore,
Hence, the required LPP is as follows:
Maximize Z = 2x + 3y
5x+4y≤200Answered by Aaryan | 1 year ago
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