Answer to Question #247451 in Math for subiksha

Question

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 E_l(x)

 and E_v(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 34 months (i.e. x≤34). If E_l(x) - 12,000 = b(x-5.0)(x-11)(x-24), ~b>0  and E_v(x) - 12,000 = a(x-2.2)^2(x-5.0)(x-25), ~a>0. If Vinay and Liala have been blacklisted together for atleast N times in 34 months, then find the value of N

Answer 1

$$E_l(x) - 12000 = b(x-5.0)(x-11)(x-24),$$

$$0\leq x\leq34$$

$$E_l(x) - 12000:x\in(5, 11)\cup(24, 34]$$

$$E_v(x) - 12000 = a(x-2.2)^2(x-5.0)(x-25),$$

$$0\leq x\leq34$$

$$E_v(x) - 12000:x\in[0, 2.2)\cup(2.2, 5)\cup(25, 34]$$

Then

$$x=26,27,28, 29, 30, 31, 32, 33, 34$$

Vinay and Liala have been blacklisted together for $N=9$ times in 34 months.