TECHNOLOGY FOCUS - BIOTECHNOLOGY - Preferred Oleaginous Microbial Cell: The oleaginous microbial cell comprises an exogenous gene, and where optionally, an endogenous desaturase of the oleaginous microbial cell has been inactivated or mutated to have less enzymatic activity. The fatty acid profile of the triglyceride oil is similar to the triglyceride oil profile of a naturally occurring oil selected from cocoa butter, coconut oil, palm oil, palm kernel oil, shea butter, beef tallow and lard. The fatty acid profile of the triglyceride oil comprises a profile selected from the total combined amounts of C8:0 and C10:0 is at least 10%, the total combined amount of C10:0, C12:0, and C14:0 is at least 50%, the total combined amount of C16:0, C18:0 and C18:1 is at least 60%, the total combined amount of C18:0, C18:1 and C18:2 is at least 60%, the total combined amount of C14:0, C16:0, C18:0 and C18:1 is at least 60%, and the total combined amount of C18:1 and C18:2 is less than 30%. The fatty acid profile of the triglyceride oil comprises a ratio of fatty acids selected from C8:0 to C10:0 ratio of at least 5 to 1, C10:0 to C12:0 ratio of at least 6 to 1, C12:0 to C14:0 ratio of at least 5 to 1, C14:0 to C12:0 ratio of at least 7:1, and C14:0 to C16:0 ratio of at least 1 to 2. The endogenous desaturase is selected from stearoyl acyl-carrier-protein (ACP) desaturase and delta 12 fatty acid desaturase. The exogenous gene is selected from a gene encoding an acyl-ACP thioesterase. The exogenous gene encodes an acyl-ACP thioesterase selected from, but not limited to, Umbellularia californica fatty acyl-ACP thioesterase (GenBank #AAC49001); Cinnamomum camphora fatty acyl-ACP thioesterase (GenBank #Q39473); U. californica fatty acyl-ACP thioesterase (GenBank #Q41635); Myristica fragrans fatty acyl-ACP thioesterase (GenBank #AAB71729); M. fragrans fatty acyl-ACP thioesterase (GenBank #AAB71730); Elaeis guineensis fatty acyl-ACP thioesterase (GenBank #ABD83939); E. guineensis fatty acyl-ACP thioesterase (GenBank #AAD42220); Populus tomentosa fatty acyl-ACP thioesterase (GenBank #ABC47311); Arabidopsis thaliana fatty acyl-ACP thioesterase (GenBank #NP172327); and A. thaliana fatty acyl-ACP thioesterase (GenBank #CAA85387). The oleaginous microbial cell further comprises a gene encoding a sucrose invertase. The oleaginous microbial cell is a cell of a microalgal genus or species selected from, but not limited to, Achnanthes orientalis, Agmenellum, Amphiprora hyaline, Amphora coffeiformis, Amphora coffeiformis punctata, Amphora coffeiformis taylori, Amphora coffeiformis tenuis, Amphora delicatissima, Amphora delicatissima capitata, Amphora sp., and Anabaena. The oleaginous microbial cell is a cell of the genus Prototheca, i.e. Prototheca moriformis. The oleaginous microbial cell is an oleaginous yeast cell or oleaginous bacterial cell. The naturally occurring oil is cocoa butter and where the exogenous gene comprises a Carthamus tinctorus thioesterase gene. The naturally occurring oil is coconut oil. The naturally occurring oil is palm oil and where the exogenous gene comprises an E. guineensis thioesterase gene, a Cuphea hookeniana thioesterase gene, a combination of a C. hookeniana KAS IV gene and a Cuphea wrightii FATB2 gene, or a construct designed to disrupt an endogenous KAS II gene. The naturally occurring oil is palm kernel oil and where the exogenous gene comprises a combination of a C. wrightii FATB2 gene and a construct designed to disrupt an endogenous SAD2B gene. The naturally occurring oil is shea butter. The naturally occurring oil is beef tallow. The naturally occurring oil is lard and where the exogenous gene comprises a combination of U. californica thioesterase gene and a construct designed to disrupt an endogenous SAD2B gene, a combination of a Gancinia mangostana EXAMPLE - No suitable example given.