Question

On a typical long distance call you talk for 30 minutes. On a typical local call you talk for 10 minutes. Your phone company offers a special low rate of $0.08 per minute for long distance calls and $0.03 per minute for local calls, for customers who spend at least 240 minutes on the phone per month. Your parents have set a limit of no more than 15 long distance calls per month and 30 local calls per month. How many minutes of long distance and local calls should you make to qualify for the specialrate plan and minimize your phone bill?

Answer 1

The number of long distance calls to be made can be obtained by linear programming

• To minimize the phone bill, the number of long distance call to be made is none

Reason:

Maximum number of number of long distance calls = 15

Maximum number of local calls = 30

Number of minutes of calls to make each month = 240 minutes

Duration of each long distance call = 30 minutes

Duration of each local call = 10 minutes

Cost of long distance call = $0.08

Cost of local call = $0.03

Solution:

Let X, represent the number of long distance calls, and let Y represent the number local calls

The objective function is given as follows;

• P = 0.08·(30)·X + 0.03·(10)·Y

P = 2.4·X + 0.3·Y

The constraints are;

X ≥ 0

Y ≥ 0

X ≤ 15

Y ≤ 30

30·X + 10·Y ≥ 240

Solving we have;

• Y ≥ 24 - 3·X

The above inequality can be plotted with MS Excel

From the objective function, P = 2.4·X + 0.3·Y, the coefficient of the long

distance calls, X is larger than the coefficient of the local calls Y, therefore,

making the minimum possible number of long distance calls of 0, and 24

local calls will give a cost;

• P = 2.4 × 0 + 0.3 × 24 = 7.2

Therefore, to minimize the phone bill, the number of long distance calls to

be made is zero long distance calls

Learn more about linear optimization here:

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