Question

A company produces two types of presentation goods A and B that requires gold and sliver. Each unit of type A requires 3 g of sliver and 1g of gold while B requires 1 g of sliver and 2 g of gold. The company can produce 9 g of sliver and 8 g of gold. Each unit of type A brings a profit of RS 40 and that type B a profit of Rs 50, determine the number of units of each type that should be produced in order to maximize profit.

Answer 1

We have that type A requires 3g of silver and 1g of gold and type B requires 1g of silver and 2g of gold.

Silver is 9g, gold is 8g.

Let type A be x and type B be y. Therefore we have

$3x+y\le9$

$x+2y\le8$

$x\ge0, y\ge0$

Type A gives profit 40Rs and type B gives profit 50Rs. Thus

$40x+50y= z$ (max this profit)

Solving for two inequalities:

$3x+y\le9$

$x+2y\le8 \implies x\le2 \ and\ y\le3$

Thus max profit would be: $40\cdot2+50\cdot3=230$

Answer: 230