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fgiga [73]
3 years ago
15

The total mass of Abdul and his baby brother is 15.25kg . The mass of Abdul and his father is 72.25kg . The mass of Abdul's fath

er is 13 times as heavy as Abdul's baby brother. What is Abdul's mass?
Mathematics
1 answer:
Helen [10]3 years ago
8 0
A+b=15.25

a+f=72.25, since f=13b

a+13b=72.25  so now we have two equation in two variables...

a+13b=72.25 and a+b=15.25  so we can say:

(a+13b=72.25)-13(a+b=15.25)

a+13b-13a-13b=72.25-198.25

-12a=-126

a=10.5 kg

So Abdul's mass is 10.5 kilograms.
  
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Step-by-step explanation:

This linear programming problem can be formulated as two inequalities (in addition to the usual constraints that the variables be non-negative). One of these expresses the constraint on weight. Let f and c represent numbers of food and clothing containers, respectively.

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The other expresses the limit on volume.

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<u>Feasible Region vertex</u>

We can subtract the boundary line equation of the first inequality from that of 5 times the second to find f:

  5(20f +5c) -(40f +25c) = 5(7000) -21000

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The second boundary line equation can be rearranged to find c:

  c = 1400 -4f = 466 2/3

The nearest integer numbers to these values are ...

  (f, c) = (233, 467)

The other vertices of the feasible region are associated with one or the other variable being zero: (f, c) = (0, 840) or (350, 0).

<u>Check of Integer Solution</u>

Trying these in the constraint inequalities gives ...

  • 40·233 +25·467 = 20,995 < 21000
  • 20·233 +5·467 = 6995 < 7000

<u>Selection of the Answer</u>

The answer to the question will be the feasible region vertex that maximizes the number of people helped. That is, we want to maximize ...

  p = 13f + 6c

The values of p at the vertices are ...

  p = 13·233 + 6·467 = 5831

  p = 13·0 + 6·840 = 5040

  p = 13·350 + 6·0 = 2100

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