Return to the Super Sleep problem of Exercise 10-7, and suppose now that we wish to plan over a 2-week time horizon. Customer demands remains 160 and 700 in the first week, but they are predicted to be 300 and 810 in the second. There is no initial inventory, but matresses may be held in the warehouse at $10 per week. All other parameters are the same in each week as those given in Exercise 10-7.

(a) Formulate a time-expanded linear program to determine an optimal shipping and holding plan.

(b) Use class optimization software to compute an optimal solution to your LP.

(c) Show that your LP can be represented as a minimum cost flow model (with total supply = total demand) by sketching the corresponding digraph and labeling as in Exercise 10-1.