Simon Tech is a software company which specializes in customized programming services, particularly focusing in solutions

for the banking industry. For any given project, the company may hire programmers in different countries of the world

through one of three setups, depending on the project$$s duration: under setup A$,$ a programmer is hired for two months

at $$2,300$ per month; under setup B$,$ a programmer is hired for three months at $$2,400$ per month; and under setup C$,$ a

programmer is hired for four months at $$2,500$ per month. The longer contract periods are more expensive as usually a

freelance programmer is usually not willing to commit to a project for a long period of time.

Over the first eight months of next year, Simon has estimated the following needs for programmers. January: $12,$ February:

$25,$ March: $19,$ April: $17,$ May: $20,$ June: $14,$ July: $10,$ and August: $11.$ Simon wants to plan for staffing their projects

up until August. The company$$s quality control program requires each programmer to receive training at the time of

hire. The training program is required even if the programmer worked for the company in a past project. The cost of

training is estimated at $$850$ per programmer hired, regardless of the length of the contract. Also, as a second component

of quality control, Simon requires full$-$time employees to monitor the work of part$-$timers. These full$-$time employees do

not work directly on the projects $($they are not part of the required number of programmers mentioned above$),$ are paid

a bonus of $$2,000$ per month for their monitoring work, and each of them is in charge of monitoring a group of five or less

programmers $($part$-$timers$)$ on any given month.

$1.$ Formulate a linear program $($algebraic formulation$)$ to help Simon determine the number of programmers to hire

each month on each setup $($contract$)$ type, as well as the number of full time employees dedicated to monitoring, in

order to meet the estimated needs at the minimum total cost. show all constraints for everything

$2.$ Build an Excel spreadsheet model of your algebraic formulation with appropriate use of SUMPRODUCT functions and

using the $$good$$ spreadsheet practices.

$3.$ Run Excel$$s built$-$in Solver to find the optimal solution and generate Answer and Sensitivity reports.

$4.$ Answer the questions at the end of this document.

Some Questions

$1.$ What is the optimal hiring plan?

$2.$ What are the different costs incurred? $($hiring and training$).$

$3.$ Is the constraint for demand of programmers in June binding? What is the interpretation of the shadow price?

$4.$ What would be the change in the optimal cost if Simon required a full$-$timer to monitor four programmers or less?

$5.$ What would be the change in the optimal cost if we forced the variables to take integer values? Is the cost decreasing

or increasing? Why?