Simplify this problem -4(3-1)+2
2 answers:
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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:
Using proportions, it is found that the total volume of the glass is of 216 cm³.
<h3>What is the missing information?</h3>The problem is incomplete, but researching it on a search engine, it is found that:
- Initially, the glass is 1/3 full.
- After adding 63 cm³ of orange of juice, the glass is 5/8 full.
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Considering the volume of the glass as x, and the information given in the problem, the following equation can be built:
We solve for x to find the volume of the glass as follows:
Then, applying cross multiplication:
7x = 24 x 63
Simplifying by 7:
x = 24 x 9
x = 216 cm³.
The total volume of the glass is of 216 cm³.
More can be learned about proportions at brainly.com/question/24372153
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