6) Liala and Vinay both have to travel to various locations for advertising their company's products. The company reimburses their expenses such as accommodation, food etc. The company also blacklists an employee whenever the employee's expenditure in a given month exceeds 12000. The accounts department fits the data of monthly expenditure to the polynomial El(x) and Ev(x) (in) for Liala and Vinay respectively, where x is the number of months since they joined the company (i.e., x = 1 represents the completion of one month). The polynomial fit is known to be applicable for a period of 31 months (i.e. x<= 31). If El(x) -12,000= b(x-5.5)(x-11)(x-24), b> 0 and Ev(x) - 12,000 = a(x- 2.0)^2 (x-5.5)(x-23), a> 0.
If Vinay and Liala have been blacklisted together for atleast N times in 31 months, then find the value of N. 3 points
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