Find the minimum value of C subject to the given constraints C = 2 x + 5 yConstraints: x + y ≥ 2 2 x − 3 y ≤ − 6 3 x − 2 y ≥ 6A. − 42B. − 4C. − 49D. − 10

Question

Find the minimum value of C subject to the given constraints  C  =  2  x  +  5  yConstraints:  x  +  y  ≥  2  2  x  −  3  y  ≤  −  6  3  x  −  2  y  ≥  6A.   −  42B.   −  4C.   −  49D.   −  10

Tianna Deleon · Accepted Answer

The answer should be   42. We can see that   4 is not correct as an answer because there is no   (  x  ,  y  )  ∈  Rsuch that   2  x  +  5  y  =  4.If  2  x  +  5  y  =  4    ⟺    y  =  −      2    5    x  +      4    5    ,then we have  x  +  y  ≥  2    ⟺    x  +      (    −          2      5        x    +          4      5        )    ≥  2    ⟺    x  ≥  2and  2  x  −  3  y  ≤  −  6    ⟺    2  x  −  3      (    −          2      5        x    +          4      5        )    ≤  −  6    ⟺    x  ≤  −      9    8    .There is no   x  ∈  R such that &quot;  x  ≥  2     and     x  ≤  −      9    8  &quot;.In the same way as above, we can see that there is no   (  x  ,  y  )  ∈  R such that   2  x  +  5  y  =  10. On the other hand, since   2  ×  6  +  5  ×  6  =  42, we can choose   42 as an answer.

Find the minimum value of C subject to the given constraints C = 2 x + 5 y

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