Question

Security at sporting events is very​ important, but it is also costly.​ Scott's Security has the contract to provide security at a high school football game this Friday. Scott must determine how many security personnel he should schedule for that night. He is attempting to maximize his​ surplus, which equals the level of​ security, measured on a​ 1-to-100 scale, minus his cost of scheduling security personnel. The security​ level, SEC​, is equal​ to: SEC left parenthesis x right parenthesis equals StartFraction left parenthesis 100 x squared minus 20 right parenthesis Over left parenthesis x squared plus 4 right parenthesis EndFraction where x is the number of security personnel. Scott pays each of his employees ​$8.40 per game that they​ work, so​ Scott's total cost is 8.40x. ​Scott's total surplus equals the level of security minus his total​ cost, or: Surplus left parenthesis x right parenthesis equals StartFraction left parenthesis 100 x squared minus 20 right parenthesis Over left parenthesis x squared plus 4 right parenthesis EndFraction minus 8.40 x . The​ surplus-maximizing number of security​ personnel, x​*, that Scott should hire for this​ Friday's game is nothing.

Answer 1

As given , the cost of Scott's expenditure or wage payment to each security personal is $8.40 per game and the total size of the football stadium if 100 square meter. It is also given that a security personal can monitor an area of amounting up to 4 square meter.

Therefore, the number of security personal needed = 100 sq. m / 4

= 25

Now, since Scott has to pay $8.40 to each security personal, therefore the total cost of Scott in employing the 25 security personals in the stadium will be =

= 25 x $ 8.40

= $ 210

Now, Scott will therefore has to demand anything above $210 from the organizers to earn surplus or profit from his business.