# A Company is Making Two Products a and B. the Cost of Producing One Unit of Products .The Company Wants to Minimize the Cost of Production by Satisfying the Given Requirements. - Mathematics

Sum

A company is making two products A and B. The cost of producing one unit of products A and B are Rs 60 and Rs 80 respectively. As per the agreement, the company has to supply at least 200 units of product B to its regular customers. One unit of product  A  requires one machine hour whereas product B has machine hours available abundantly within the company. Total machine hours available for product A are 400 hours. One unit of each product A and B requires one labour hour each and total of 500 labour hours are available. The company wants to minimize the cost of production by satisfying the given requirements. Formulate the problem as a LPP.

#### Solution

Let the company produces x units of product A and y units of product B.
Since, each unit of product A costs Rs 60 and each unit of product B costs Rs 80.Therefore, x units of product A and y units of product B will cost Rs 60x and Rs 80y respectively.
Let Z denotes the total cost.

∴ Z = Rs (60x + 80y)
Also, one unit of product A requires one machine hour.
The total machine hours available with the company for product A are 400 hours.
Therefore, $x \leq 400$

This is our first constraint
Also,one unit of product A and B require 1 labour hour each and there are a total of 500 labours hours.
Thus, $x + y \leq 500$
​This is our second constraint.
Since, x and y are non negative integers, therefore

$x, y \geq$ 0 Also, as per agreement, the company has to supply atleast 200 units of product B to its regular customers.
$\therefore y \geq 200$  Hence, the required LPP is  as follows:
Minimize Z = 60x + 80y
subject to  x $\leq$ 400
x +y  $\leq$ 500
$y \geq 200$
$x, y \geq$  0
Concept: Introduction of Linear Programming
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 30 Linear programming
Exercise 30.1 | Q 2 | Page 14