Answer:
Remember that a set is a base for some topology on
if satisfy the following properties:
1.
2. For , If
then exist
such that
.
Now, for we verify the above properties:
1. It's clear that
2. Let . Without loss of generality suppose that
. Then
, this implies that
and
and
.
Then, B satisfy the two properties. This show that B is a basis for a topology in
The number of long distance calls to be made can be obtained by linear programming
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 = 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;
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;
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:
