How to minimise this function and get initial conditions

[Bharatisha]

How to minimise this function and get initial conditions . I have the answer for initial conditions.
ra = min(00237 − 0000175v + 8.693f − 000159y)
subjected to

124.53 ≤ v ≤ 167.03
0.025 ≤ f ≤ 0.083
6.2 ≤ y ≤ 14.8

v= 144.2 , f = 0.025, y = 9.5 How to get this?

 

[HallsofIvy]

How to minimise this function and get initial conditions . I have the answer for initial conditions.
ra = min(00237 − 0000175v + 8.693f − 000159y)
subjected to

124.53 ≤ v ≤ 167.03
0.025 ≤ f ≤ 0.083
6.2 ≤ y ≤ 14.8

v= 144.2 , f = 0.025, y = 9.5 How to get this?

You can't get this, it is NOT the correct answer.

This is a linear function, defined on a convex set (a rectangular solid, actually). Different values of "ra" represent different planes parallel to one another. If the plane corresponding to a given value of ra passes inside the rectangular solid, we can decrease ra slightly by moving the plane parallel to itself. This is true until the plane passes outside the rectangular solid. It little thought should show you that the last point of the rectangular solid the planes touches will be a vertex (or and entire edge if two vertices give the same value).

So a minimum value for a linear function on a polygonal solve (such as a rectangular solid) must occur at a vertex! Here, it is easy to see that "v= 144.2, f= 0.025, y= 9.5" does NOT give a minimum value because no vertex has "v= 144.2" or "y= 9.5".

(your given function is "00237 − 0000175v + 8.693f − 000159y". What do those coefficients without a decimal point mean? Is "00237" just 237 or .00237 or 0.0237?)