Refer the textbook 12th ed, page number 43 and Q19 for similar problem Kim Davis

Question

Refer the textbook 12th ed, page number 43 and Q19 for similar problem Kim Davis has decided to purchase a cellular plan, but she is unsure about which rate plan to select. The "regular" plan charges a fixed fee of $55 per month for 1000 minutes of airtime plus 0.33 per minute for any time over 1000 minutes. The "executive" plan charges a fixed fee of $100 per month for 1200 minutes of airtime plus $ 0. 40 per minute over 1200 minutes If Kim expects to use the phone for 21 hours per month which plan should she select? At what level of use would Kim be indifferent between the two plans? If Kim expects to use the phone for 1600 minutes and above per month, which plan should she select? As a management science expert, how do you help her choose the right plan for all minutes?

Explanation / Answer

Q.2 Lets say kim use x hours talktime per month

Regular Plan charges = 55 + 0.33 * (60x - 1000)

Executive Plan charges = 100 + 0.40 * ( 60x - 1200)

(a) Kim expects to use 21 hours per month

so Regular Plan charges = 55 + 0.33 * (60 * 21 - 1000) = $140.8

Executive Plan charges = 100 + 0.40 * ( 60 * 21 - 1200) = $124

so Executive plan is better.

(b) let say the value is X so the charges will be the same

55 + 0.33 * (60x - 1000) = 100 + 0.40 * ( 60x - 1200)

55 + 19.8x - 330 = 100 + 24x - 480

4.2x = 105

x = 25 Hrs

(c) Kim selects to use the phone for 1600 minutes and above per month.

Regular Plan charges = 55 + 0.33 * (1600 - 1000) = $253

Executive Plan charges = 100 + 0.40 * ( 1600 - 1200) = $260

so Regular plan would be better.

d) As a management science expert, we can see that the regular plan charges would be better for more than 25 Hours and executive plan charges would be better for less than 25 Hours.

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