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.

Answer 1

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 formulat​ion of the given linear programmimg problem is 
Max Z =  \[40x + 50y\] 

subject to

\[3x + y \leq 9\]

\[x + 2y \leq 8\]

\[x, y \geq 0\]