Consider a chocolate manufacturing company that produces only two types of chocolate - A and B. Both the chocolates require Milk and Choco only. To manufacture each unit of A and B, the following quantities are required:

Each unit of A requires 1 unit of Milk and 3 units of Choco

Each unit of B requires 1 unit of Milk and 2 units of Choco

The company kitchen has a total of 5 units of Milk and 12 units of Choco. On each sale, the company makes a profit of P 6 per unit A sold P 5 per unit B sold.

Now, the company wishes to maximize its profit. How many units of A and B should it produce respectively?

Solution:

	Milk	Choco	Profit per unit
A	1	3	6
B	1	2	5
TOTAL	5	12

Let X is total number of units produced by A

Let Y is total number of units produced by A and Z is the total profit

how to calculate the total profit of the company

just multiply the total number of units A and B produced and Per unit profit

6 and 5 respectively

so Profit Max Z=6X+5Y

That means we need to maximize the profit z

The company will try to maximize the profit by producing as many as units of A and B

but the problem is Milk and Choco resources are limited from the table,

A and B need 1 unit of Milk

But the Milk is available only 5 units

how to represent this in mathematically

X+Y<=5

And

each unit of A, B need 3 ,2 units of Choco

but total amount of Choco is only 12 units again,

represent it mathematically

3X+2Y<=12

A can only integer value

and we have 2 more constraints

X>=0

Y>=0

Therefore, X=2, Y=3

Z= 6X+5Y

Z= 6*2+5*3

Z=27

Question:

How to prepare the Graphical Solution of the Problem?