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Question
A company produces two types of articles A and B which requires silver and gold. Each unit of A requires 3 gm of silver and 1 gm of gold, while each unit of B requires 2 gm of silver and 2 gm of gold. The company has 6 gm of silver and 4 gm of gold. Construct the inequations and find feasible solution graphically.
Solution
Let the company produces x units of article A and y units of article B.
The given data can be tabulated as:
| Article A (x) |
Article B |
Availability | |
| Gold | 1 | 2 | 4 |
| Silver | 3 | 2 | 6 |
Inequations are:
x + 2y ≤ 4 and 3x + 2y ≤ 6
x and y are number of items, x ≥ 0, y ≥ 0
First we draw the lines AB and CD whose equations are x + 2y = 4 and 3x + 2y = 6 respectively.
| Line | Equation | Points on the X-axis | Points on the Y-axis | Sign | Region |
| AB | x +2y = 4 | A(4, 0) | B(0, 2) | ≤ | origin side of line AB |
| CD | 3x + 2y = 6 | C(2, 0) | D(0, 3) | ≤ | origin side of line CD |
The feasible solution is OCPBO, which is shaded in the graph.
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