Suppose that a warehouse has been designed based on cubic footage to hold $100,000$ "cubes" of space for product storage. Once the warehouse was operating at what was considered an efficient level of productivity, only $85,000$ cubes of space were routinely occupied.

a$.$ What is the design utilization?

b$.$ Name some reasons why the warehouse might only operate at $85\%$ of design capacity $($or $85\%$ capacity utilization$).$

Note: A $90\%$ utilization factor is typical of warehousing operations that are operated in the traditional fork lift manner.

Suppose that you have had a restaurant for the past $2$ years. The first year was about what was expected $($sales of $$200,000$ for the $300$ days that you were open$).$ Trofits were fair, but a critical time for the restaurant is approaching. Demand for service on Friday and Saturday nights $($biggest sales nights of the week$)$ has exceeded the capacity to serve customers, and some have been turned away or decided to eat elsewhere. When the restaurant is serving at capacity $($like on Friday and Saturday nights$),$ you estimate that total sales would be $$600,000$ per year.

$($a$)$ What is the restaurant's design capacity utilization figure?

$($b$)$ Is that good or bad given the nature of the weekend demand for restaurant business? Why?

$($c$)$ What do you suggest be done to improve capacity utilization?

$($d$)$ You have been considering building on an addition to the restaurant in anticipation that you would have even greater demand in the future. Your decision is simple: expand the building or remain the same size. However, you are not sure of the demand that will result after you expand. Demand may increase quite a bit or be relatively flat. You estimate the probability of increasing demand significantly at $30\%,$ increasing modestly at $50\%$ and staying the same at about $20\%.$ Estimated profits that would result $($after amortizing the building expansion$)$ at each demand level is $$70,000$ at significantly increasing demand; $$10,000$ at modest increases in demand; and a loss of $$20,000$ if demand stays the same. What would be the expected profit of making the decision to build the addition?