Management of High Tech Services $($HTS$)$ would like to develop a model that will help allocate their technicians' time between service calls to regular contract customers and new

customers. A maximum of $80$ hours of technician time is available over the two$-$week planning period. To satisfy cash flow requirements, at least $$800$ in revenue $($per technician$)$ must be

generated during the two$-$week period. Technician time for regular customers generates $$25$ per hour. However, technician time for new customers only generates an average of $$8$ per

hour because in many cases a new customer contact does not provide billable services. To ensure that new customer contacts are being maintained, the techniclan time spent on new

customer contacts must be at least $60\%$ of the time spent on regular customer contacts. Given these revenue and policy requirements, HTS would like to determine how to allocate

technician time between regular customers and new customers so that the total number of customers contacted during the two$-$week period will be maximized. Technicians require an

average of $50$ minutes for each regular customer contact and $1$ hour for each new customer contact.

$($a$)$ Develop a linear programming model that will enable HTS to allocate technician time between regular customers and new customers. $($Let $R$ be the time allocated to regular

customer service and let $N$ be the time allocated to new customer service.$)$

Max$1\mathrm{.}2R+N$

$s.t.$

Hours of technician time

Revenue generated

Time spent on customer contact

$R,N0$

$($b$)$ Find the optimal solution. What is the objective value at the optimal solution?

$at(R,N)=()$