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.

Answer 1

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 (y)	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.