Consider the transshipment model from Section $7\mathrm{.}4,$ except now suppose the demands are binary. That is$,$ the demands can only equal $0$ or $1,$ and they are governed by a Bernoulli distribution: images with probability images and images with probability images $,$ for images $.$ All of the remaining assumptions from Section $7\mathrm{.}4\mathrm{.}2$ hold.

Your goal in this problem will be to formulate the expected cost and evaluate several feasible values for the base$$stock levels images $.$ Assume that images must be an integer.

Explain why images $.$

For each possible solution images below, write the expected values of the state variables images $,$ images $,$ images $,$ and images $,$ and then write the expected cost images $.$

images

images

images

images

$($The cases in which images or images are similar to the cases above, so we'll skip them.$)$

Hint $1$: If images $,$ that does not mean that stage i never orders!

Hint $2$: To check your cost functions, we'll tell you the following: If images $,$ images $,$ and images for all images $,$ then images $,$ images $,$ images $,$ and images $.$ Note, however, that these parameters do not satisfy the assumptions on page $26.$