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EDIT: Several comments have pushed for direct data on the question of relative prices. According to Galenson in late 17th century Barbados, an adult male slave cost around £20 while a young girl might be closer to £10, sometimes less. Meanwhile, Eltis discusses some relevant estimates of yearly provisions for slaves and servants for around the same time, mostly in the range of £1 to £5 per year. Whether this data shows that underfeeding slaves fit some kind of rational cost-benefit analysis for some planters or not, I have absolutely no idea.

EDIT: Several comments have pushed for direct data on the question of relative prices. According to Galenson in late 17th century Barbados, an adult male slave cost around £20 while a young girl might be closer to £10, sometimes less. Meanwhile, Eltis discusses some relevant estimates of yearly provisions for slaves and servants for around the same time, mostly in the range of £1 to £5 per year. Whether this data shows that underfeeding slaves fit some kind of rational cost-benefit analysis for some planters or not, I have absolutely no idea. Particularly on the lower end of food cost estimates, this is assuming slaves grow some significant portion of their own food. So to try to make such a cost-benefit analysis would require an understanding of the opportunity costs involved in taking slaves away from sugar production. I'm not sure if anyone with relevant expertise has looked at this in any detail. Unless someone can find such an analysis, I think the best resolution to this question would be to simply prove whether or not Olusoga accurately represents something Sloane wrote or not.

EDIT: Several comments have pushed for direct data on the question of relative prices. According to Galenson in late 17th century Barbados, an adult male slave cost around £20 while a young girl might be closer to £10, sometimes less. Meanwhile, Eltis discusses some relevant estimates of yearly provisions for slaves and servants for around the same time, mostly in the range of £1 to £5 per year. Whether this data shows that underfeeding slaves fit some kind of rational cost-benefit analysis for some planters or not, I have absolutely no idea.

Ultimately the more germane question though is about British 17th-century slave plantations in general. It is easy to fin systematic studies of mortality patterns on slave plantations such as this one about the US South and this one on Trinidad. These generally apply to the 18th and 19th centuries, rather than the 17th. They do show periods of high mortality, and some evidence to suggest malnutrition was at least a contributing cause.

Ultimately the more germane question though is about British 17th-century slave plantations in general. It is easy to find systematic studies of mortality patterns on slave plantations such as this one about the US South and this one on Trinidad. These generally apply to the 18th and 19th centuries, rather than the 17th. They do show periods of high mortality, and some evidence to suggest malnutrition was at least a contributing cause.