Break Even Analysis

[ardenarden]

I want to purchase a cell phone but am unsure about which plan to select.
1st plan charges a fixed fee of $55 per month for 1,000 minutes + $0.33 per min for antime over 1,000 minutes.
2nd plan charges of fixed fee of $100 per month for 1,200 minutes + $0.25 per min over 1,200.
Question:
#1) If I expect to use the phone for 21 hours per month, which plan should I select?
#2) At what level of use would I be indifferent between the two plans?

For #1 - I know I think I should use this formula but need help resolving
TC= Total Cost
N = Number of Additional Minutes above 1200
VC=Variable Costs (Price per Additional Minute)
FC= Fixed Cost (Cost of Plan)

For #2 - I know I need to set each plan to equal each other but I need help solving.

Thank you!

 

[arthur ohlsten]

plan 1 cost = 55 +.33[21(60)-1000]

plan2 cost = 100 + .25[21(60)-1200

solve plan 1 cost
solve plan 2 cost

see which is cheaper. I think plan 2 is cheaper
=====================================================================================
let x = the minutes you will use the phone
plan 1 cost = 55 + .33 [x-1000]
plan 2 cost = 100 +.25[x-1200]

when does plan1 equal plan 2?
55+.33[x-1000]= 100 + .25[x-1200]
55 +.33x-330=100+.25x-300
.33x-275=-200+.25x
.08x=75
x=7500/8
x=937.5 minutes answer


Arthur

 

[mmm4444bot]

?

Arthur's function definitions only work on restricted domains because each plan is modeled by a piecewise function. We cannot equate expressions whose domains differ.

Anyway, it should be obvious that 937.5 minutes of monthly use does not cost the same under each plan because this level of minutes lies below both thresholds for initiating per-minute surcharges.

In other words, people who use 937.5 minutes under plan 1 pay $55; people who use 937.5 minutes under plan 2 pay $100.

I hope that the original poster has not already turned in somebody else's work as their own. (Or, maybe I don't.)

?

 

[ardenarden]

Thank you!!