Some mutations (or 'major genes') have a desirable effect in heterozygous carriers but an undesirable effect in homozygous carriers. When these mutations affect a trait of significant economic importance, their eradication, depending on their effect and frequency, may be counterproductive. This is especially the case of major genes affecting the ovulation rate and thus the prolificacy in meat sheep populations. To manage such situations, a mating design based on the major genotypes of reproducers has to be optimized. Both the effect of the major gene and the cost of genotyping candidates at this locus influence the expected genetic progress and profitability of the breeding plan. The aim of this study was to determine the optimal combination of matings that maximizes profitability at the level of the whole population (nucleus + commercial flocks). A deterministic model was developed and, using sequential quadratic programming methodology, the optimal strategy (optimal combination of matings) that maximized the economic gain achieved by the population across a range of genotype effects and genotyping costs was determined. The optimal strategy was compared with simpler and more practical strategies based on a limited number of parental genotype mating types. Depending on the genotype effect and genotyping costs, the optimal strategy varied, such that either the heterozygous frequency and/or polygenic gain was maximized with a large number of animals genotyped, or when genotyping costs were higher, the optimization led to lower heterozygous frequency and/or polygenic gain with fewer animals genotyped. Comparisons showed that some simpler strategies were close to the optimal strategy. An overlapping model was then derived as an application of the real case of the French Lacaune meat sheep OVI-TEST breeding program. Results showed that a practical strategy based on mating non-carriers to heterozygous carriers was only slightly less effective than the optimal strategy, with a reduction in efficiency from 3% to 8%, depending on the genotyping costs. Based on only two different parental genotype mating types, this strategy would be easy to implement.