How would you guys work this problem out

a manager in a call center needs to determine how many agents to schedule next week. based on previous data she expects to get 7940 calls next week the following conditions apply

on average, call center agents can handle seven calls an hour,
the call enter is open 10 hours 5 days a week
full time agents work 40 hours a week but are only on call for 35 hours per week
part time agents work 20 hours a week but are only on calls 17 hours per week

which combination is best to meet the scheduling needs

a 15 fulltime me agents and 15 part time agents

b. 20 full time agents and 7 part time agents

c. 20 full time agents and 20 part time agents

d 25 full time agents and 5 part time agents

e 28 full time agents and 10 part time agents

Answer with explanation:

Number of calls expected in next week by manager = 7940

Average Number of calls that call center agent will attend in an hour =7 calls

It is also given that, Call center remain open for 10 hours 5 days a week.

Also, it is given that, full time agents work 40 hours a week but are only on call for 35 hours per week  ,Part time agents work 20 hours a week but are only on calls 17 hours per week .

⇒Number of hours worked by full time agents × Number of calls attended in an hour × Number of full time agents + Number of hours worked by Part time agents × Number of calls attended in an hour × Number of Part time agents ≤ 7940

⇒35 × 7×Number of full time agents +17 × 7 ×Number of Part time agents ≤ 7940

Option A

⇒35×15×7+17×7×15

= 3675+1785

= 5460

Option B

⇒35 ×7×20+17×7×7

=4900 +833

= 5733

Option C

⇒35×20×7 +17×20×7

=4900+2380

=7280

Option D

⇒25 × 35×7+17×7×5

=6125 +595

=6720

Option E

⇒28×35×7+17×7×10

=6860+1190

=8050

Option E, ⇒ 28 full time agents and 10 part time agents , is best to meet the scheduling needs is most appropriate, that is nearer to 7940 calls.