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Question
A company produces two types of goods A and B, that require gold and silver. Each unit of type A requires 3 g of silver and 1 g of golds while that of type B requires 1 g of silver and 2 g of gold. The company can procure a maximum of 9 g of silver and 8 g of gold. If each unit of type A brings a profit of Rs 40 and that of type B Rs 50, formulate LPP to maximize profit.
Solution
Let x goods of type A and y goods of type B were produced.
Number of goods cannot be negative.
Therefore,
\[x, y \geq 0\]
The given information can be tabulated as follows:
| Silver( gm) | Gold white (gm) | |
| Type A | 3 | 1 |
| Type B | 1 | 2 |
| Availability | 9 | 8 |
Therefore, the constraints are
\[3x + y \leq 9\]
\[x + 2y \leq 8\]
If each unit of type A brings a profit of Rs 40 and that of type B Rs 50.Then, x goods of type A and y goods of type Bbrings a profit of Rs 40x and Rs 50y.
Total profit = Z = \[40x + 50y\] which is to be maximised.
Thus, the mathematical formulation of the given linear programmimg problem is
Max Z = \[40x + 50y\]
subject to
\[3x + y \leq 9\]
\[x + 2y \leq 8\]
\[x, y \geq 0\]
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