We will apply the quantum-inequality-type restrictions to Alcubierre's warp drive metric on a scale in which a local region of spacetime can be considered `flat'. These are inequalities that restrict the magnitude and extent of the negative energy which is needed to form the warp drive metric. From this we are able to place limits on the parameters of the `warp bubble'. It will be shown that the bubble wall thickness is on the order of only a few hundred Planck lengths. Then we will show that the total integrated energy density needed to maintain the warp metric with such thin walls is physically unattainable.