A locally isolated thermophile, Geobacillus sp. SAB-40, producing thermostable extracellular amylase constitutively and an induced intracellular ${eta}$-galactosidase was characterized and identified based on 16S rRNA sequencing. A phylogenetic analysis then revealed its closeness to Geobacillus stearothermophilus. To evaluate the effect of the culture conditions on the coproduction of both enzymes by G stearothermophilus SAB-40, a Plackett-Burman fractional factorial design was applied to determine the impact of twenty variables. Among the tested variables, $CaCI_2$, the incubation time, $MgSO_4{cdot}7H_2O$, and tryptone were found to be the most significant for encouraging amylase production. Lactose was found to promote ${eta}$-galactosidase production, whereas starch had a significantly negative effect on lactase production. Based on a statistical analysis, a preoptimized medium attained the maximum production of amylase and ${eta}$-galactosidase at 23.29 U/ml/ min and 12,958 U/mg biomass, respectively, which was 3-and 2-fold higher than the yield of amylase and lactase obtained with the basal medium, respectively.