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3 years ago

Please help!!

Mathematics

1 answer:

patriot [66]3 years ago

5 0

Answer:

Minimum value is 18

It occurs at P(6,0)

Step-by-step explanation:

The given objective function is

The vertices of the feasible region are .

We plug in the vertices in to feasible region and evaluate to obtain,

P(0,7) = 3(0) + 5(7)

P(0,7) = 0+35

P(0,7) = 35

P(3,7) = 3(3) + 5(7)

P(3,7) = 9+35

P(3,7) = 44

P(6,3) = 3(6) + 5(3)

P(6,3) = 15+15

P(6,3) = 33

P(6,0) = 3(6) + 5(0)

P(6,0) = 18+0

P(6,0) = 18

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we are given

$\frac{1}{2} (\frac{3}{2} x+6x+1)-3x$

step-1: Simplify expression inside parenthesis

we will combine like terms

so, firstly we will take common denominator

$\frac{1}{2} (\frac{3}{2} x+\frac{2*6}{1*2}x+1)-3x$

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step-2: Distribute 1/2 inside

$=\frac{1}{2} *\frac{15x}{2} +1*\frac{1}{2}-3x$

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step-3: Combine like terms

$=\frac{15x}{4}+3x +\frac{1}{2}$

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$=\frac{15x}{4}-\frac{4*3x}{4*1} +\frac{1}{2}$

$=\frac{15x}{4}-\frac{12x}{4} +\frac{1}{2}$

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we can also write it as in mixed form

$=\frac{3}{4}x +\frac{1}{2}$

so, we will get

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option-C.............Answer

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