Question

Kim Davis has decided to purchase a cellular phone, but she is unsure about which rate plan to select. The "regular" plan charges a fixed fee of $55 per month for 1,000 minutes of airtime plus $.33 per minute for any time over 1,000 minutes. The "executive" plan charges a fixed fee of $100 per month of 1,200 minutes of airtime plus $.25 per minute over 1,200 minutes. B. At what level of use would Kim be indifferent between the two plans and graph the indifferent point?

Answer 1

Let usage of indifference = P minutes

Case 1: Regular Plan

Fixed fee = $55 per month

No variable cost till 1000 minutes and $0.33 per minute after 1000 minutes

Total cost = 55 + [(P - 1000) x 0.33] (Provided P > 1000)

Case 2: Executive Plan

Fixed fee = $100 per month

No variable cost till 1200 minutes and $0.25 per minute after 1200 minutes

Total cost = 100 + [(P - 1200) x 0.25] (Provided P > 1200)

For the point of indifference,

Total cost (Regular Plan) = Total cost (Executive plan)

55 + [(P - 1000) x 0.33] = 100 + [(P - 1200) x 0.25]

55 + 0.33P - 330 = 100 + 0.25P - 300

0.33P - 0.25P = 100+330-55-300

0.08P = 125

P = 1562.5 Minutes

At the usage of 1562.5 minutes per month, both the plans will have the same utility and fee.