Cox Cable Company needs to lease warehouse storage space for five months at the start of the year. It knows how much space will be required in each month. However, since these space requirements are quite different, it may be economical to lease only the amount needed each month on a month-by-month basis. On the other hand, the monthly cost for leasing space for additional months is much less than for the first month, so it may be desirable to lease the maximum amount needed for the entire five months. Another option is the intermediate approach of changing the total amount of space leased (by adding a new lease and/or having an old lease expire) at least once but not every month. Two or more leases for different terms can begin at the same time.

The space requirements (in square feet) and the leasing costs (in dollars per thousand square feet) are given in the tables below.

Month	Space requirements	Lease length	Lease cost
Jan	15,000	1 month	$280
Feb	10,000	2	450
Mar	20,000	3	600
April	5000	4	730
May	25,000	5	820

The task is to find a leasing schedule that provides the necessary amounts of space at the minimum cost.

A.) Determine the optimal leasing schedule and the optimal total cost.

B.) Consider what happens when the cost of a 5-month lease (currently $820) changes. Construct a graph showing how the optimal total cost varies with the cost of a 5-month lease, over the range from $800 to $1000.

C.) Consider instead what happens when the timing of space requirements shifts. In particular, suppose that March requirements drop and April requirements rise by the same amount. Construct a table to show, for shift amounts up to 15,000 square feet, how the shift alters the optimal total cost.

1. a) Describe the qualitative pattern in the solution.

2. (b) Usethepatternin(a)totracetheeffectsofincreasingthespacerequiredfor

   January. How will the leasing schedule change? How will the total cost change per square foot of increase? Verify this cost in the Sensitivity Report.

3. (c) For how much of a change in Januarys requirement will the pattern in(b) persist? Confirm this change in the Sensitivity Report.