1 | initial version |

Here is some progress, but not very much:

```
sage: var('a b c d e n k')
(a, b, c, d, e, n, k)
sage: eqs = (
....: a + b == n*(c + d),
....: b == k*e,
....: a >= 80,
....: b >= 1000,
....: c >= 20,
....: d >= 40,
....: a + b <= 2000,
....: c + d <= 90
....: )
....:
sage: result = solve(eqs, (a,b,c,d,e,n,k)) # takes a while; be patient
sage: for r in result:
....: print "--"
....: for t in r:
....: print " ", t
# ... huge amount of output ...
```

I tried constraining `n`

and `k`

to take on integer values via:

```
sage: assume(n, "integer")
sage: assume(k, "integer")
```

... before calling `solve`

, but it does not help.

2 | corrected for typo in original post |

Here is some progress, but not very much:

`sage: var('a b c d `~~e ~~n k')
(a, b, c, d, ~~e, ~~n, k)
sage: eqs = (
....: a + b == n*(c + d),
....: b == ~~k*e,
~~k*d,
....: a >= 80,
....: b >= 1000,
....: c >= 20,
....: d >= 40,
....: a + b <= 2000,
....: c + d <= 90
....: )
....:
sage: result = solve(eqs, ~~(a,b,c,d,e,n,k)) ~~(a,b,c,d,n,k)) # takes a while; be patient
sage: for r in result:
....: print "--"
....: for t in r:
....: print " ", t
# ... huge amount of output ...

I tried constraining `n`

and `k`

to take on integer values via:

```
sage: assume(n, "integer")
sage: assume(k, "integer")
```

... before calling `solve`

, but it does not help.

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