We prove a Johns theorem for simplices in Rᵈ with positive dilation factor $d+2$, which improves the previously known d² upper bound. This bound is tight in view of the d lower bound. Furthermore, we give an example that d isn't the optimal lower bound when $d=2$. Our results answered both questions regarding Johns theorem for simplices with positive dilation raised by {leme2020costly}.
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Lu Zhou (2020) studied this question.