Linear Optimization equation system: A post office requires different numbers of...

[reagon3]

Hey folks!

I'm really frustrated because it's nearly impossible to find the equations for the following situation:

QUESTION 3
A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in the table. Union rules state that each full-time employee must work five consecutive days and then receive two days off. The post office wants to meet its daily requirements using only full-time employees. Formulate and solve an LP that the post office can use to minimize the number of full-time employees that must be hired.

Day
Monday 17
Tuesday 13
Wednesday 15
Thursday 19
Friday 14
Saturday 16
Sunday 11


What i understood from above is that need at least 19 employes (highest value) for covering the thursday. But how does the referring equation system look like? I really have no clue. I'm not interested in the "employee solution" but how to create the right equations. (i guess there are 8 - 7 for the days and 1 for the aspect of minimizing?)

Many Thanks in advance!

 

[Ishuda]

Hey folks!

I'm really frustrated because it's nearly impossible to find the equations for the following situation:

QUESTION 3
A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in the table. Union rules state that each full-time employee must work five consecutive days and then receive two days off. The post office wants to meet its daily requirements using only full-time employees. Formulate and solve an LP that the post office can use to minimize the number of full-time employees that must be hired.

Day
Monday 17
Tuesday 13
Wednesday 15
Thursday 19
Friday 14
Saturday 16
Sunday 11


What i understood from above is that need at least 19 employes (highest value) for covering the thursday. But how does the referring equation system look like? I really have no clue. I'm not interested in the "employee solution" but how to create the right equations. (i guess there are 8 - 7 for the days and 1 for the aspect of minimizing?)

Many Thanks in advance!

First of all you have a total sum for man-days in a 7 day period. Since each employee can only give 5 man-days each 7 day period, you have a minimum number of employees. Will that minimum actually work and meet union rules? I don't know right off hand.

 

[Steven G]

First of all you have a total sum for man-days in a 7 day period. Since each employee can only give 5 man-days each 7 day period, you have a minimum number of employees. Will that minimum actually work and meet union rules? I don't know right off hand.

People-days not man-days lol