Question 944250


plan A is 39.99 per month plus .25 * x over 450


plan B is 59.99 per month plus .30 * x over 900.


plan C is 99.99 per month + .35 * x over 1500.


These look like split functions or what are otherwise called piecewise defined functions.


for Plan A, the function would be:


y = 39.99 for 0 <= x <= 450
y = 39.99 + .25 * (x - 450) for x > 450


for Plan B, the function would be:


y = 59.99 for 0 <= x <= 900
y = 59.99 + .30 * (x - 900) for x > 900


For plan C, the function would be:


y = 99.99 for 0 <= x <= 1500
y = 99.99 + .35 * (x - 1500) for x > 1500


Smith uses 750 minutes per month.
Jones uses 1350 minutes per month.


you would analyze each plan at 750 minutes per month for Smith.
you would analyze each plan at 1350 minutes per month for Jones.


For Smith who uses 750 minutes per month:


Plan A costs 39.99 + .25 * (750 - 450) = 39.99 + .25 * 300 = 114.99
Plan B costs 59.99
Plan C costs 99.99


cheapest plan for Smith is plan B.


For Jones who uses 1350 minutes per month:


Plan A costs 39.99 + .25 * (1350 - 450) = 39.99 + .25 * 900 = 264.99
Plan B costs 59.99 + .30 * (1350 - 900) = 59.99 + .30 * 450 = 217.49
Plan C costs 99.99


cheapest plan for Jones is plan C.