BUT I REQUIRE VALUE SHOULD BE

F <1.250

G>2.220

I suspect that the best way to deal with those constraints is to generate the random values in VBA, iterating until a combination of random A, B, C and D is found that is within the constraints on F and G.

On second thought, I believe we can avoid using VBA with the following formula for C:

=RANDBETWEEN( MAX( D1-20, ROUNDUP(0.48*B1*A1*D1/1250, 0) ), MIN( D1+20, INT(0.48*B1*A1*D1*$H$2/2220) ) )
where H1 is "H", and H2 ("hFactor") is

=(6700 - 5*H1) * (1/(500-H1) - 1/(800-H1)) * 0.9 .

However, if you know H > 18.1457802973919 (+4.62E-14) is always true, we can get by with just:

=RANDBETWEEN( MAX( D1-20, ROUNDUP(0.48*B1*A1*D1/1250,0) ), D1+20 )
The MAX expression ("min C") is necessary to ensure F < 1.25.

The MIN expression ("max C") is necessary to ensure G > 2.22 . But G > 2.22 is always true for all H > 18.1457802973919 (+4.62E-14) ("min H").

Caveat: If 0.48*B1*A1*D1/1250 is an exact integer, we should use ROUNDUP(...)+1. Likewise, if 0.48*B1*A1*D1*$H$2/2220 is an exact integer, we should use INT(...)-1. I did not include those additional tests because I suspect they are never(?) true.

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The derivation of those limits is complicated; probably TMI for most readers.

Min C is derived as follows, substituting the formulas for F and E:

F < 1.25

0.48*B*A/E / 1000 < 1.25

0.48*B*A*D / (C*1000) < 1.25

0.48*B*A*D / 1250 < C

Max C is derived as follows, substituting the formulas for G and F:

G > 2.22

hFactor * F > 2.22

hFactor * 0.48*B*A*D / (C*1000) > 2.22

hFactor * 0.48*B*A*D / 2220 > C

where hFactor is the subexpression in the formula for G, to wit:

hFactor = (6700 - 5*H) * ( 1/(500-H) - 1/(800-H) ) * 0.9

Min H to allow for the simplified RANDBETWEEN expression is derived as follows:

J1, min H:

__to be determined__
J2, hFactor: =(6700 - 5*J1) * (1/(500-J1) - 1/(800-J1)) * 0.9

J3, min F by G: =2.22/J2

J4: min F: =0.48*B1*A1*D1 / ((D1+20)*1000)

J5, goal: =J4-J3

Solver set-up:

Set objective: J5

To value: 0

By changing: J1

Note that Solver returns an estimate, due to internal limitations. So I manually tweek the result in J1 in order to derive a more precise min H. For that purpose, I use =SUM(J4,-J3) in J5 in order to avoid dubious arithmetic tricks by Excel.

The formula in J3 is derived from G = hFactor*F > 2.22 .

The formula in J4 is based on the "min F" formula in posting #7, where A1 is min A (117), B1 is min B (10.8), D1 is min D (68), and D1+20 is the corresponding max C.