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The corner points of the feasible region...

The corner points of the feasible region determined by the following system of linear inequalities: `2x+ylt=10 ,\ x+3ylt=15 ,\ x ,\ ygeq0\ a r e\ (0,0),\ (5,0),(3,\ 4)a n d\ (0,5)dotL e t\ Z=p x+q y ,\ w h e r e\ p ,\ q >0` . Condition on `p\ a n d\ q` so that the maximum of Z occurs at both (3,4) and (0,5) is `p=q` b. `p=2q` c. `p=3q` d. `q=3p`

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(d) Maximum value of `Z` is unique. Given that the maximum value of `Z` is obtained at two points `(3,4)` and `(0,5)`.
`:.` Value of `Z` at `(3,4)=` value of `Z` at `(0,5)`
`impliesp(3)+q(4)=p(0)+q(5)`
`implies3p+4q=5qimplies3p=q`
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