(See Solution) Suppose HTS allocate X hours to regular customers and Y hours to new customers. Total number of customers can be contacted as per the allocation
Question: Suppose HTS allocate X hours to regular customers and Y hours to new customers.
Total number of customers can be contacted as per the allocation is:
\[Z=\frac{60X}{50}+Y=1.2X+Y\] (Note that the technicians require an average of 50 minutes for each regular customer contact and 1 hour for each new customer contact)Constraints :
Maximum technician time available is 80 hours \[\Rightarrow X+Y\le 80\]
Minimum revenue to be generated is $800 \[\Rightarrow 25X+8Y\ge 800\]
The condition that the technician time spent on new customer contacts must be at least 60% of the time spent on regular customer contacts \[\Rightarrow Y\ge 0.60X\Rightarrow Y-0.60X\ge 0\]
Non-Negativity restrictions \[X\ge 0\] and \[Y\ge 0\]
Thus the LPP becomes:
Maximize \[Z=1.2X+Y\]
Subject to \[X+Y\le 80\]
\[25X+8Y\ge 800\] \[Y-0.60X\ge 0\] \[X\ge 0\] , \[Y\ge 0\]
Deliverable: Word Document 