A businessman needs five cabinets, 12 desks and 18 shelves cleaned out. He has two part time employees, Rashid and Ruby. Ruby can clean one cabinet, three desks and three shelves in a day while Rashid can clean one cabinet, two desks and 6 shelves in one day. Rashid is paid Rs. 22 per day and Ruby is paid Rs. 25 per day. In the order to minimize the cleaning costs, for how many days should Rashid and Ruby be employed? Formulate the problem as a linear programming problem and find its solution by the graphical method.

To formulate this problem as a linear programming problem, let's define some variables and set up the objective function and constraints.

Let:
- \(x\) be the number of days Rashid is employed.
- \(y\) be the number of days Ruby is employed.

The objective of the businessman is to minimize the cleaning costs, which can be represented as the total cost (\(C\)):

\[
C = 22x + 25y
\]

The objective function is to minimize \(C\).

Now, we need to set up the constraints based on the cleaning requirements and the limitations:

1. Cabinet Cleaning Constraint:
   Ruby can clean one cabinet per day, and Rashid can also clean one cabinet per day. The businessman needs five cabinets cleaned.
   So, the cabinet cleaning constraint is: \(x + ________ _____ ____ _______ _________ _________ ____ _________ __________.
_______ _____ ______ ________ ___ _________ _________ ___ _________ _____ ____.
________ _____ ______ _______ ___ _____ __________.
_____ ________ ________ ______ __________ ______ _____ _________ ________ ________ ___.
__________ ___ __________ _________ ________ ____ ________ _______ ____ _________ ______.
_____ ____ _________ _______ __________ __________ ___ _____ _____ ____ _________ ______.
________ __________ _____ __________ _____ ______ _____ _______ _____ ______ __________ ______.
_________ _______ ________ _________ _____ _____ _____ ______ _______ ____ _______.
_____ __________ _________ _______ _____ _________ _____ _______ ____ __________ ____ ____.
_______ ______ ______ __________ _________.
________ ______ _____ _________ __________.
______ __________ _________ __________ ____.
____ __________ ____ ________ ___ ___ ________ _______ ________ ________ ____ _________.
_____ __________ _________ _____ _______ ____.
_____ _________ _________ ___ ________ __________ _____ ________ ___.
_____ ___ ___ ___ ________ ___ _________ ________ __________ __________.
_______ _____ ___ _________ _________ _________ _________ _______ _______ ____ __________.
____ ___ _________ _________ ____ ______ __________.
____ ___ _______ _________ _______ ______ _____.
______ ___ ________ ______ ____ _________ ________ _____ ______ ______ __________.
_____ _________ ________ ________ _________ __________ ___ ____ _________ _____.
__________ _______ ________ _________ _________ __________ ________.
_____ ___ ______ ________ _______ ____ _______ _________ ___ __________ ______.
_____ _______ _________ _______ __________ ________ ______ ___ _________ _______ ___.
________ __________ ___ ____ _____.
________ ________ __________ _________ ______ __________ ________ ________ _________.
_______ ________ __________ ________ __________ ____ ______ _____ ____ ____.
__________ ___ _______ ____ ________ _____ ______ ______ ________ ___.
______ ___ __________ _________ _________.
_________ _____ ________ _________ ____ ____ ___.
____ __________ _________ ______ _______ ______ ________.
___ _____ _______ ________ ___.
______ ____ ___ _________ ______ ______ __________.
_________ ___ ___ ______ ___ ______ ____ ______ _____.
______ ________ ____ __________ ____ ___ ________.
____ _____ ___ ___ _______ _______ __________ ____ _____ _____.
_________ __________ ____ ____ _______ ________.
____ _______ ___ ________ ________ __________.
___ ______ _______ ______ _____ ________ ________ ____ _______.
____ _____ __________ _____ ________ ____ _______ _________ _______ ________ _________ _______.
_______ _________ _________ ______ ______ ________ _____ _______.
____ ____ _____ _______ _______ ___ ________.
___ ______ _________ _____ ________ ______ __________ ___ ____ ________ _________ __________.
__________ ____ _______ _____ ____ ______ ___ _________.
___ ______ _______ ______ _____.
_______ _____ _____ _________ _________ _________.
_______ _______ ________ ___ _____ _________ ________.
_______ __________ ____ _________.
Get Full Answer on WhatsApp