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astraxan [27]
3 years ago
11

Please help me with this question

Mathematics
1 answer:
Tamiku [17]3 years ago
3 0

9514 1404 393

Answer:

  1/2, 3/10

  1/21, 8/27

Step-by-step explanation:

Fractions are multiplied by multiplying the numerators and expressing that product over the product of the denominators:

 \dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{ac}{bd}

In several cases here, the numerator product has factors in common with the denominator product. Those can be cancelled, reducing the product fraction to lowest terms.

  \dfrac{3}{4}\times\dfrac{2}{3}=\dfrac{3\cdot2}{4\cdot3}=\dfrac{3\cdot2}{3\cdot2\cdot2}=\boxed{\dfrac{1}{2}}\\\\\dfrac{4}{5}\times\dfrac{3}{8}=\dfrac{4\cdot3}{5\cdot8}=\dfrac{4\cdot3}{4\cdot2\cdot5}=\boxed{\dfrac{3}{10}}\\\\\dfrac{1}{6}\times\dfrac{2}{7}=\dfrac{1\cdot2}{6\cdot7}=\dfrac{2}{2\cdot3\cdot7}=\boxed{\dfrac{1}{21}}\\\\\dfrac{4}{9}\times\dfrac{2}{3}=\dfrac{4\cdot2}{9\cdot3}=\boxed{\dfrac{8}{27}}

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Answer:

z (min)  = 705

x₁  = 10

x₂  = 9

Step-by-step explanation:

Let´s call  x₁  quantity of food I ( in ou )  and x₂ quantity of food II ( in ou)

          units of vit. C   units of vit.E   Cholesterol by ou

x₁                 32                      9                         48

x₂                16                      18                          25

Objective function z

z  =   48*x₁   +  25*x₂        To minimize

Subject to:

1.-Total units of vit. C at least  464

32*x₁   +  16*x₂     ≥   464

2.- Total units of vit. E at least  252

9*x₁  + 18*x₂   ≥  252

3.- Quantity of ou per day

x₁   +   x₂   ≤  35

General constraints    x₁  ≥ 0    x₂   ≥ 0

Using the on-line simplex method solver (AtoZmaths) and after three iterations the solution is:

z (min)  = 705

x₁  = 10

x₂  = 9

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