Cost minimization in call center hiring

CAT 2005 Slot 1 · QA · Hard · Algebra

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A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and female operators get a fixed wage of Rs. 250 and Rs. 300 per day respectively. In addition, a male operator gets Rs. 15 per call he answers and a female operator gets Rs. 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job?

  1. A.

    15

  2. B.

    14

  3. C.

    12

  4. D.

    10

Answer

D

Explanation

Let mm be male operators, ff be female operators. Calls equation: 40m+50f=100040m + 50f = 1000. Cost per male operator =250+40×15=850= 250 + 40 \times 15 = 850. Cost per female operator =300+50×10=800= 300 + 50 \times 10 = 800. Total cost C=850m+800fC = 850m + 800f. Given 7<f≤127 < f \le 12. From 40m+50f=1000  ⟹  4m+5f=10040m + 50f = 1000 \implies 4m + 5f = 100. Possible integer pairs (f,m)(f, m) for f∈{8,9,10,11,12}f \in \{8, 9, 10, 11, 12\}:

  • If f=8f = 8, 4m=60  ⟹  m=154m = 60 \implies m = 15. Cost =850(15)+800(8)=12750+6400=19150= 850(15) + 800(8) = 12750 + 6400 = 19150.
  • If f=12f = 12, 4m=40  ⟹  m=104m = 40 \implies m = 10. Cost =850(10)+800(12)=8500+9600=18100= 850(10) + 800(12) = 8500 + 9600 = 18100. Minimum cost occurs when m=10m = 10.

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