Answer :
To solve this integer program, you can use optimization software such as AMPL, as mentioned in the hint. The software will find the optimal values for the decision variables (x1, x2, x3, x4, x5, x6, x7) that minimize the objective function while satisfying the constraints. To solve this problem as an integer program, we can set up the following model:
Decision Variables:
Let x1 represent the number of telemarketers starting work on Monday.
Let x2 represent the number of telemarketers starting work on Tuesday.
Let x3 represent the number of telemarketers starting work on Wednesday.
Let x4 represent the number of telemarketers starting work on Thursday.
Let x5 represent the number of telemarketers starting work on Friday.
Let x6 represent the number of telemarketers starting work on Saturday.
Let x7 represent the number of telemarketers starting work on Sunday.
Objective:
Minimize the total number of employees needed to fulfill the daily requirements.
Constraints:
x1 + x4 + x5 + x6 + x7 >= 23 (for Monday)
x1 + x2 + x5 + x6 + x7 >= 16 (for Tuesday)
x1 + x2 + x3 + x6 + x7 >= 21 (for Wednesday)
x1 + x2 + x3 + x4 + x7 >= 17 (for Thursday)
x1 + x2 + x3 + x4 + x5 >= 20 (for Friday)
x2 + x3 + x4 + x5 + x6 >= 12 (for Saturday)
x3 + x4 + x5 + x6 + x7 >= 15 (for Sunday)
Bounds:
x1, x2, x3, x4, x5, x6, x7 >= 0 (integer)
This model ensures that the minimum number of telemarketers is scheduled each day to meet the required daily targets. The objective is to minimize the total number of employees needed across the week.
The calculation and solution of this integer program require the use of optimization software and cannot be provided within the scope of a text-based response.
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