(A) The cost of plan B would be less expensive for Damy, if Damy makes 20 transactions per month on average.
(B) The minimum number of transactions that Damy would need to make in a month to justify getting the unlimited plan (Plan B) is 16.
Computed using cost equations for plan A and plan B.
How is a cost equation formed?
A cost equation is the sum of the fixed cost and the product of the per unit cost to the number of units.
Thus, the Cost equation = Fixed cost + per unit cost * number of units.
How to solve the question?
We are given two plans for Damy's chequing accounts.
Plan A: $2.95 per month plus $0.65 transaction
Plan B: $13.25 per month for unlimited transactions
We assume the number of transactions made by Damy monthly to be x.
Thus, the cost equation for Damy for:-
Plan A:
Cost equation = Fixed cost + per unit cost * number of units.
Thus, the cost equation = 2.95 + 0.65*x,
or, the cost equation = 2.95 + 0.65x.
Plan B:
Cost equation = Fixed cost + per unit cost * number of units.
Thus, the cost equation = 13.25 + 0*x,
or, the cost equation = 13.25.
Question (A):
In the question, we are asked for the plan which will be less expensive for Damy, if Damy makes 20 transactions per month on average.
To check for the less expensive plan, we put the number of transactions, that is, x, as 20 in the cost equations for both the plans to get the less costly plan.
Thus, Cost of plan A for 20 transactions = 2.95 + 0.65*20 = 2.95 + 13 = $15.95.
Thus, Cost of plan B for 20 transactions = $13.25.
Thus, the cost of plan B would be less expensive for Damy, if Damy makes 20 transactions per month on average.
Question (B):
In the question, we are asked for the minimum number of transactions that Damy would need to make in a month to justify getting the unlimited plan (Plan B), that is, we need to find the minimum value of x for which cost equation for plan A is greater than the cost equation for plan B.
This can be shown as:
Cost equation of plan A > Cost equation of plan B,
or, 2.95 + 0.65x > 13.25,
or, 0.65x > 13.25 - 2.95,
or, 0.65x > 10.30,
or, x > 10.30/0.65,
or, x > 15.85 (approx.)
Thus, the minimum number of transactions that Damy would need to make in a month to justify getting the unlimited plan (Plan B) is 16.
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