Question

 Consider a chocolate manufacturing company which 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, 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

 . Rs 6 per unit A sold

 . Rs 5 per unit B sold.

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

 Model the problem in a linear programming formulation. What are the decision variables? What is the objective function? What are the constraints? What are the restrictions for the decision variables?

Answer 1

Solution

Let’s construct the table to represent the problem

	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 also

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

If the company wants to make maximum profit, they should satisfy the inequalities mentioned

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all the best