Please help to solve this problem. I am new to this type of problems and any help will be greatly appreciated
$$\text{ Minimize } 7x-5y+3z$$
$$\text{ Such that } \ \ \ 0 ≤ x ≤ 6 , -2 ≤ y ≤ 7 , -4 ≤ z ≤ 9$$
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1I see. Since the volume specified is a brick shape, you just need to check the function at the 8 corner points. – Will Jagy Aug 12 '14 at 23:17
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For practice, in the plane rectangle $0 \leq x \leq 6, ; -2 \leq y \leq 7,$ minimize $3x- 2y.$ You can draw a picture. – Will Jagy Aug 12 '14 at 23:21
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Thanks very much will Jagy I sort of see what you are saying, but can not work out how 7x - 5y- +3z will be minimized at the corner points – Gamini Amerasinghe Aug 12 '14 at 23:32
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Well, please do the easier 2 variable example, including drawing on graph paper. You are correct in thinking that there is some detail for you to learn before you know instantly that only a corner works; in more general problems that need not be true, even in a planar problem you could have the minimum at two corners and the entire line segment between them. On the rectangle I gave, minimize $x$ itself! – Will Jagy Aug 12 '14 at 23:39
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Another option is simply to try and get a feel for what increasing/decreasing $x,y,z$ does. As $x$ increases, the function increases. As $y$ increases, the function decreases. What does changing $z$ do? Can you now see which $(x,y,z)$ point must be the answer? – Aug 13 '14 at 01:11