Question

Q1. Paul has recently upgraded his smartphone and is now looking to upgrade his data plan. The flat rates are shown in the table below. The amount over the maximum allowable gigabyte (GB) for each plan are charged $15 per GB, fractional amounts included. Yunsik is uncertain how many GB he might use because of the new phone’s additional features, but his best bet is 10GB, which doesn’t align directly with any plan.

Plan	Base price	Max # of GB
A	$60	5
B	$85	7
C	$140	12
D	$150	15

a (3 points). If Paul uses 10GB of data, which should he choose?

b (3 points). At what level of usage should Paul upgrade from “Plan B to Plan C” and “Plan C to Plan D”

c (4 points). Summarize the decision rules for when Paul should choose each plan.

Answer 1

a)

If Paul uses 10 GB of data then as per the plan details given Paul should either go for Plan B or C with max # of GB of 7 and 12 respectively. The other two options will either not give sufficient GB (Plan A) or lot of wastage of GB/ base charge (Plan D).

We will calculate cost of Plan B and C for 10 GB usage

Plan B - Base plan will give 7 GB and rest need to be on actual usage per GB.

So total cost = base price + usage cost = 85 + (10-7)*15 =$130

Plan C - Max allowed is sufficient for 10 GB

So total cost = base price =$140

Hence plan B has a lower cost so Paul should choose Plan B.

b)

To calculate at what Paul should upgrade the plan, we will calculate the breakeven points for total cost

Plan B to Plan C

Point should be between 7 and 12 GB.

Total cost of Plan B = Total plan of Plan C

85 + (X-7)*15 = 140

X= 10.67GB

Hence, Paul should upgrade from Plan B to Plan C if usage is more than 10.67GB

Plan C to D

Point should be between 12 and 15 GB.

Total cost of Plan C = Total plan of Plan D

140 + (X-12)*15 = 150

X= 12.67GB

Hence, Paul should upgrade from Plan C to Plan D if usage is more than 12.67GB

c)

We wll also calculate at what point Paul should upgrade from Plan A and Plan B

Point should be between 5 and 7 GB.

Total cost of Plan A = Total plan of Plan B

60 + (X-5)*15 = 85

X= 6.67GB

Decision rule for each plan will be as below

- Plan A for usage upto 6.67GB

- Plan B for usage higher than 6.67 GB and up to 10.67 GB

- Plan C for usage higher than 10.67 GB and up to 12.67 GB

- Plan D for usage higher than 12.67 GB

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