The best and most economical approach is (4) Homozygous transgenic mice should be mated with wild type mice for continued production of transgenic heterozygous offspring.

Genetic logic

Let T be the transgene and t wild type.

• Homozygous transgenic mice: TT

• Wild-type mice: tt

Cross TT × tt:

• All F₁ progeny: Tt (heterozygous, transgenic).

• Each generation, repeating TT × tt gives 100% Tt, providing a continuous supply of heterozygous transgenics.

This is efficient and requires only maintaining a homozygous transgenic stock plus a wild-type stock.

Option-wise analysis

1. More transgenic founders should be generated.

   • Producing new founders is labor‑intensive and costly.

   • It does not solve the maintenance problem once homozygotes become infertile.

2. Crossing transgenic mice with wild type in earlier generations.

   • This would create heterozygotes, but unless a clear TT stock is established, you would still need genotyping each generation and might lose the line.

   • The question asks what to do now that homozygotes are infertile; earlier crossings do not address ongoing maintenance as directly as option 4.

3. Inbreeding should be avoided after 5th generation.

   • Avoiding further inbreeding doesn’t automatically give a steady stream of heterozygotes; it just reduces additional inbreeding depression.

   • It is not a concrete breeding scheme.

4. Homozygous transgenic mice should be mated with wild-type mice – correct.

   • This straightforward cross yields only heterozygous transgenic offspring each generation.

   • It is genetically simple, economical, and ensures the line continues even though TT males or females are infertile for breeding among themselves.

Therefore, the most preferable and economical approach is option (4).