Leasing Warehouse Space: Cox Cable Company needs to lease warehouse storage space for 5 months at...

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Leasing Warehouse Space: Cox Cable Company needs to lease warehouse storage space for 5 months at the start of the year. It knows how much space will be required in each month, and it can purchase a variety of lease contracts to meet these needs. For example, it can purchase 1-month leases in each month from January to May. It can also purchase 2-month leases in January through April, 3-month leases in January through March, 4-month leases in January and February, or a 5-month lease in January. In total, there are 15 possible leases it could use. It must decide which leases to purchase and how many square feet to purchase on each lease. Since the space requirements differ month to month, 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 5 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 two tables below. Month January February March April May Requirements 15,000 10,000 20,000 5,000 25,000 Lease length 1 month 2 months 3 months 4 months 5 months Lease cost 280 450 600 730 820 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) Trace the effects of increasing the space required for January. How will the leasing schedule change? How will the total cost change? Leasing Warehouse Space: Cox Cable Company needs to lease warehouse storage space for 5 months at the start of the year. It knows how much space will be required in each month, and it can purchase a variety of lease contracts to meet these needs. For example, it can purchase 1-month leases in each month from January to May. It can also purchase 2-month leases in January through April, 3-month leases in January through March, 4-month leases in January and February, or a 5-month lease in January. In total, there are 15 possible leases it could use. It must decide which leases to purchase and how many square feet to purchase on each lease. Since the space requirements differ month to month, 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 5 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 two tables below. Month January February March April May Requirements 15,000 10,000 20,000 5,000 25,000 Lease length 1 month 2 months 3 months 4 months 5 months Lease cost 280 450 600 730 820 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) Trace the effects of increasing the space required for January. How will the leasing schedule change? How will the total cost change?