Can you please create a linear programming solution using th

Can you please create a linear programming solution using the information below.   This is a practice problem so please add any information that may be missing.

Customer’s contact our call center when they have questions. We need to determine how many reps we need in order to be able to answer our customer calls while keeping our personnel costs to a minimum.

Linear Programming would be helpful in our call center in order to minimize our total personnel costs while still being able to answer our customer calls. We have 11 full time employees and we currently have 7 full time temporary employees on the staff. Let’s say the full time employees earn $176 per day and the full time temporary workers earn $224 per day. If we receive 382 customer calls per day and the average talk time for each call is 6 minutes. How many reps would be needed on the phones to assist customers.

In formulating the LP, the objective is to have the appropriate staff level in order to be able to answer customer inquiries in a timely manner at minimal personnel costs. Our constraints are that the average talk time per call is 6 minutes. Since our full time employees cost less per day, we would want to make sure we use our 11 full times employees first to assist with calls and add the appropriate number of full time temporary workers as needed.

Solution

Available full time 11 @176 per day

Temporary full time 7 @224 per day

Customer calls 382

Talk time 6

Total talk time = 382*6 =2292

11 full time employees must be fully engaged to attend these calls first.

Let us assume full time employees work 6hours a day(excluding lunch, tea time)

In 8 hours they can attend 6*60/6 = 36 customers per day

For 11 full time they can attend 36*11 = 396 calls

Hence 11 full time employees can work for 6 hours per day to attend all calls without temporary workers.

Minimum cost = 176(11) per day

= 1936