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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 <em>X</em>, represent the number of long distance calls, and let <em>Y</em> 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, <em>X</em> is larger than the coefficient of the local calls <em>Y</em>, 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 <u>zero long distance calls</u>
Learn more about linear optimization here:
